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Unsolved problem in computational complexity theory
Unsolved problem in computer science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph isomorphism
Graph_isomorphism_problem
Bijection between the vertex set of two graphs
called an isomorphism class of graphs. The question of whether graph isomorphism can be determined in polynomial time is a major unsolved problem in computer
Graph_isomorphism
Mapping a graph onto itself without changing edge-vertex connectivity
of a list of generators, is polynomial-time equivalent to the graph isomorphism problem, and therefore solvable in quasi-polynomial time, that is with
Graph_automorphism
Problem in theoretical computer science
theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G {\displaystyle G} and H {\displaystyle H}
Subgraph_isomorphism_problem
Decision problem
isomorphism problem is the decision problem of determining whether two given finite group presentations refer to isomorphic groups. The isomorphism problem
Group_isomorphism_problem
Very general problem in computer science
problems including factoring, discrete logarithm, graph isomorphism, and the shortest vector problem. This makes it especially important in the theory
Hidden_subgroup_problem
constitutes a graph isomorphism. Fractional isomorphism is the coarsest of several different relaxations of graph isomorphism. Whereas the graph isomorphism problem
Fractional_graph_isomorphism
Topics referred to by the same term
Isomorphism problem may refer to: graph isomorphism problem group isomorphism problem isomorphism problem of Coxeter groups This disambiguation page lists
Isomorphism_problem
List of unsolved computational problems
quantum computer? Can the graph isomorphism problem be solved in polynomial time on a classical computer? The graph isomorphism problem involves determining
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Problem of finding similarity between graphs
and the model graph. The case of exact graph matching is known as the graph isomorphism problem. The problem of exact matching of a graph to a part of
Graph_matching
Task in computational graph theory
Clearly, the graph canonization problem is at least as computationally hard as the graph isomorphism problem. In fact, graph isomorphism is even AC0-reducible
Graph_canonization
Area of discrete mathematics
called the clique problem (NP-complete). One special case of subgraph isomorphism is the graph isomorphism problem. It asks whether two graphs are isomorphic
Graph_theory
Hungarian-American mathematician and computer scientist
in 2017. abstract We show that the Graph Isomorphism (GI) problem and the related problems of String Isomorphism (under group action) (SI) and Coset
László_Babai
Complexity class
example is the graph isomorphism problem, the graph theory problem of determining whether a graph isomorphism exists between two graphs. Two graphs are isomorphic
NP-completeness
Complexity class of problems
satisfiability problems cannot be in NPI. Some problems that are considered good candidates for being NP-intermediate are the graph isomorphism problem, and decision
NP-intermediate
Unsolved problem in computer science
NP-intermediate problems. The graph isomorphism problem, the discrete logarithm problem, and the integer factorization problem are examples of problems believed
P_versus_NP_problem
Property of graphs that depends only on abstract structure
polynomial of a graph. Easily computable graph invariants are instrumental for fast recognition of graph isomorphism, or rather non-isomorphism, since for
Graph_property
Method for solving one problem using another
-complete problem is NP-hard. Similarly, the complexity class GI consists of the problems that can be reduced to the graph isomorphism problem. Since graph isomorphism
Polynomial-time_reduction
Graph in graph theory
showed, the problem of recognizing whether a graph is a lexicographic product is equivalent in complexity to the graph isomorphism problem. The lexicographic
Lexicographic product of graphs
Lexicographic_product_of_graphs
Inherent difficulty of computational problems
Such problems are called NP-intermediate problems. The graph isomorphism problem, the discrete logarithm problem and the integer factorization problem are
Computational complexity theory
Computational_complexity_theory
Graph which is isomorphic to its complement
checking whether a given graph is self-complementary are polynomial-time equivalent to the general graph isomorphism problem. Sachs, Horst (1962), "Über
Self-complementary_graph
S2CID 119151552. Klin, M. H., M. Muzychuk and R. Poschel: The isomorphism problem for circulant graphs via Schur ring theory, Codes and Association Schemes, American
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Type of computational problem
divisible by k?". For all k≥2, ModkP contains the graph isomorphism problem. Further, the graph isomorphism problem is low in ModkP. When k is prime, the set
Counting_problem_(complexity)
Set of edges without common vertices
largest matching in a bipartite graph can be treated as a network flow problem. Finding a largest matching in a general graph is much more difficult; it can
Matching_(graph_theory)
Proving validity without revealing other data
showed that the graph nonisomorphism problem, the complement of the graph isomorphism problem, has a zero-knowledge proof. This problem is in co-NP, but
Zero-knowledge_proof
NP-complete graph problem
complexity theory and graph theory, induced subgraph isomorphism is an NP-complete decision problem that involves finding a given graph as an induced subgraph
Induced subgraph isomorphism problem
Induced_subgraph_isomorphism_problem
Estimate of time taken for running an algorithm
Subgroup Problem with Polynomial Space". arXiv:quant-ph/0406151v1. Grohe, Martin; Neuen, Daniel (2021). "Recent advances on the graph isomorphism problem". In
Time_complexity
Graphs that differ only by edge subdivision
In graph theory, two graphs G {\displaystyle G} and G ′ {\displaystyle G'} are homeomorphic if there is a graph isomorphism from some subdivision of G
Homeomorphism_(graph_theory)
Graph that can be embedded in the plane
also graph isomorphism problem). Any planar graph on n nodes has at most 8(n-2) maximal cliques, which implies that the class of planar graphs is a class
Planar_graph
Basic concept of graph theory
of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. In an undirected graph G, two vertices u
Connectivity_(graph_theory)
Methodic assignment of colors to elements of a graph
graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For example, an edge coloring of a graph is
Graph_coloring
Abstract machine that models computation
classes, consider the graph isomorphism problem, the problem of determining whether it is possible to permute the vertices of one graph so that it is identical
Interactive_proof_system
In mathematics, invertible homomorphism
an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if
Isomorphism
Topics referred to by the same term
see Sport in Ireland § Gymnastics GI, a complexity class in the graph isomorphism problem Galvanized iron Gi alpha subunit, a protein Gastrointestinal tract
GI
Cubic graph with 10 vertices and 15 edges
Unsolved problem in mathematics Conjecture: Every bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics
Petersen_graph
of a directed graph. Hamiltonian completion Hamiltonian path problem, directed and undirected. Induced subgraph isomorphism problem Graph intersection
List_of_NP-complete_problems
Task of computing complete subgraphs
problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph.
Clique_problem
popular classification criteria is graph isomorphism, not to be confused with crystallographic isomorphism. Two periodic graphs are often called topologically
Periodic_graph_(geometry)
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
polynomial-time recognition algorithm for circulant graphs, and the isomorphism problem for circulant graphs can be solved in polynomial time. Small Ramsey
Circulant_graph
Graph representing edges of another graph
isomorphisms of the graphs and isomorphisms of their line graphs. Analogues of the Whitney isomorphism theorem have been proven for the line graphs of multigraphs
Line_graph
testing whether two graphs are isomorphic. While it solves graph isomorphism on almost all graphs, there are graphs such as all regular graphs that cannot be
Colour_refinement_algorithm
Unsolved problem in mathematics Which finite groups are BI-groups? More unsolved problems in mathematics Babai's problem is a problem in algebraic graph theory
Babai's_problem
them; see isomorphism. isomorphism A graph isomorphism is a one-to-one incidence preserving correspondence of the vertices and edges of one graph to the
Glossary_of_graph_theory
Class of artificial neural networks
expressive as the Weisfeiler Leman graph isomorphism test. In practice, this means that there exist different graph structures that cannot be distinguished
Graph_neural_network
Convex hull of a finite set of points in a Euclidean space
the graph isomorphism problem. However, it is also possible to translate these problems in the opposite direction, showing that polytope isomorphism testing
Convex_polytope
Computational complexity class
n)}} . Problems for which a quasi-polynomial time algorithm has been announced but not fully published include: The graph isomorphism problem, determining
Quasi-polynomial_time
Infinite graph containing all countable graphs
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with
Rado_graph
Peruvian mathematician (born 1977)
error in the proof of the quasipolynomial time algorithm for the graph isomorphism problem that was announced by László Babai in 2015. Babai subsequently
Harald_Helfgott
possible. Finding this graph is NP-hard. In the associated decision problem, the input is two graphs G and H and a number k. The problem is to decide whether
Maximum common induced subgraph
Maximum_common_induced_subgraph
maximum common edge subgraph problem on general graphs is NP-complete as it is a generalization of subgraph isomorphism: a graph H {\displaystyle H} is isomorphic
Maximum_common_edge_subgraph
Binary operation in graph theory
In graph theory, the modular product of graphs G and H is a graph formed by combining G and H that has applications to subgraph isomorphism. It is one
Modular_product_of_graphs
Index of articles associated with the same name
In graph theory and theoretical computer science, a maximum common subgraph may mean either: Maximum common induced subgraph, a graph that is an induced
Maximum_common_subgraph
Undirected, connected, and acyclic graph
unlabeled free trees is a harder problem. No closed formula for the number t(n) of trees with n vertices up to graph isomorphism is known. The first few values
Tree_(graph_theory)
Venezuelan computer scientist
Vazirani, Luis von Ahn, and Ryan Williams. List of Venezuelans Graph isomorphism problem Non-interactive zero-knowledge proof Quantum coin flipping Pancake
Manuel_Blum
Creating a new graph from an existing graph
applied to the host graph by searching for an occurrence of the pattern graph (pattern matching, thus solving the subgraph isomorphism problem) and by replacing
Graph_rewriting
Computer algebra system
speeds for most index contractions with an approach based on the graph isomorphism problem rather than canonicalisation. Free and open-source software portal
Cadabra_(computer_program)
Graph defined from a mathematical group
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract
Cayley_graph
American mathematician and computer scientist
the University of Oregon. He is known for his research on the graph isomorphism problem and on algorithms for computational group theory. Luks did his
Eugene_M._Luks
Canadian academic
include algorithms for graphs, the development of mathematical software, the graph reconstruction problem, the graph isomorphism problem, projective geometry
William_Lawrence_Kocay
Generalization of graph theory
(i)}} The bijection ϕ {\displaystyle \phi } is then called the isomorphism of the graphs. Note that H ≃ G {\displaystyle H\simeq G} if and only if H ∗
Hypergraph
Graph made from disjoint union of complete graphs
a cluster graph is formed from cliques that are all the same size, the overall graph is a homogeneous graph, meaning that every isomorphism between two
Cluster_graph
Graph of chess rook moves
In graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's
Rook's_graph
Graph structure studied in group theory
The cycle graph of a group is not uniquely determined up to graph isomorphism; nor does it uniquely determine the group up to group isomorphism. That is
Cycle_graph_(algebra)
German computer scientist (born 1955)
these hierarchies play an important role in the complexity of the graph isomorphism problem, which Schöning further developed in a 1993 monograph with Köbler
Uwe_Schöning
Theorem classifying finite simple groups
breakthrough in the best known theoretical algorithm for the graph isomorphism problem in 1982 The Schreier conjecture The Signalizer functor theorem
Classification of finite simple groups
Classification_of_finite_simple_groups
Topics referred to by the same term
glucose-dependent insulinotropic polypeptide Genome India Project Graph isomorphism problem GSM Interworking Profile, a telecommunications standard Francisco
GIP
Graph of numbers differing by a square
x ± 4 (mod 13). The Paley graphs are self-complementary: the complement of any Paley graph is isomorphic to it. One isomorphism is via the mapping that
Paley_graph
Structure-preserving correspondence between node-link graphs
bijection, and its inverse function f −1 is also a graph homomorphism, then f is a graph isomorphism. Covering maps are a special kind of homomorphisms
Graph_homomorphism
Greek mathematician and logician (born 1947)
quantifiers, is that the graph isomorphism problem is not likely to be NP-complete (joint with R. Boppana, J. Hastad). Graph isomorphism is one of the very
Stathis_Zachos
crystal net isomorphism problem (i.e., the query whether two given crystal nets are isomorphic as graphs; not to be confused with crystal isomorphism) is readily
Periodic graph (crystallography)
Periodic_graph_(crystallography)
In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph G {\displaystyle G} , find the maximal number of edges
Forbidden_subgraph_problem
Directed graph isomorphic to its own transpose graph
to itself by the isomorphism or to group more than two vertices in a cycle of isomorphism. A path or cycle in a skew-symmetric graph is said to be regular
Skew-symmetric_graph
Number of edges touching a vertex in a graph
graph; in some cases, non-isomorphic graphs have the same degree sequence. A graph that is identified up to isomorphism by its degree sequence is called unigraph
Degree_(graph_theory)
Graph made from a subset of another graph's nodes and their edges
The induced subgraph isomorphism problem is a form of the subgraph isomorphism problem in which the goal is to test whether one graph can be found as an
Induced_subgraph
Logical formulation of graph properties
subgraph isomorphism problem for a fixed subgraph H {\displaystyle H} asks whether H {\displaystyle H} appears as a subgraph of a larger graph G {\displaystyle
Logic_of_graphs
Graph related to another graph by a covering map
graph-theoretic terms to a requirement that it be acyclic and connected; that is, a tree. The universal covering graph is unique (up to isomorphism)
Covering_graph
Erdős discrepancy problem. 2015 – László Babai finds that a quasipolynomial complexity algorithm would solve the Graph isomorphism problem. 2016 – Maryna
Timeline_of_mathematics
Subgraph with contracted edges
straightforward to verify that the graph minor relation forms a partial order on the isomorphism classes of finite undirected graphs: it is transitive (a minor
Graph_minor
Type of randomized algorithm
were introduced by László Babai in 1979, in the context of the graph isomorphism problem, as a dual to Monte Carlo algorithms. Babai introduced the term
Las_Vegas_algorithm
Professor emeritus of computer science Known for his research on the graph isomorphism problem and on algorithms for computational group theory Stephanie A.
List of University of Oregon faculty and staff
List_of_University_of_Oregon_faculty_and_staff
Chordal graph where all cycles of even length have odd chords
solved efficiently for strongly chordal graphs. Graph isomorphism is isomorphism-complete for strongly chordal graphs. Hamiltonian Circuit remains NP-complete
Strongly_chordal_graph
Yes/no problem in computer science
Every function problem can be turned into a decision problem; the decision problem is just the graph of the associated function. (The graph of a function
Decision_problem
Conjecture in graph theory
Unsolved problem in mathematics Are graphs uniquely determined by their subgraphs? More unsolved problems in mathematics In graph theory, informally, the
Reconstruction_conjecture
Family of graphs whose shallow minors are sparse graphs
algorithms for problems including the subgraph isomorphism problem and model checking for the first order theory of graphs. A t-shallow minor of a graph G is defined
Bounded_expansion
Permutation of the elements of a set in which no element appears in its original position
27 December 2011. Lubiw, Anna (1981). "Some NP-complete problems similar to graph isomorphism". SIAM Journal on Computing. 10 (1): 11–21. doi:10.1137/0210002
Derangement
Complexity class used to classify decision problems
number of times). The subgraph isomorphism problem of determining whether graph G contains a subgraph that is isomorphic to graph H. Turing machine – Computation
NP_(complexity)
algorithm can easily solve all the problems that a quantum computer can solve efficiently. The graph isomorphism problem is low for parity P ( ⊕ P {\displaystyle
Low_(complexity)
Vertices whose removal breaks all cycles
systems, and VLSI chip design. The FVS decision problem is as follows: INSTANCE: An (undirected or directed) graph G = ( V , E ) {\displaystyle G=(V,E)} and
Feedback_vertex_set
Branch of mathematics
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatorial
Algebraic_graph_theory
also called polyhedral graphs. The problem of deciding whether a given graph is polytopal or not is known as the realization problem and is NP hard in general
Graph_of_a_polytope
Computational problems no algorithm can solve
undecidable. The word problem for groups. The conjugacy problem. The group isomorphism problem. Determining whether two finite simplicial complexes are
List_of_undecidable_problems
Two closely related models for generating random graphs
result of this infinite process is (with probability 1) the same graph, up to isomorphism. Dual-phase evolution – Process that drives self-organization within
Erdős–Rényi_model
Maximum number of colors obtainable by a greedy graph coloring algorithm
chordal graphs and claw-free graphs, and also (using general results on subgraph isomorphism in sparse graphs to search for atoms) for graphs of bounded
Grundy_number
Australian mathematician (born 1951)
McKay's main contributions has been a practical algorithm for the graph isomorphism problem and its software implementation NAUTY (No AUTomorphisms, Yes?)
Brendan_McKay_(mathematician)
804655. Norris, Nancy (1995). "Universal covers of graphs: Isomorphism to depth n−1 implies isomorphism to all depths". Discrete Applied Mathematics. 56:
Fibrations_of_graphs
Graph formed by complementation and disjoint union
In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation
Cograph
Function in algebraic graph theory
claw graph and the path graph on 4 vertices. A graph is chromatically unique if it is determined by its chromatic polynomial, up to isomorphism. In other
Chromatic_polynomial
Type of sub-graph
mapping f is called an isomorphism between G and G′. When G″ ⊂ G and there exists an isomorphism between the sub-graph G″ and a graph G′, this mapping represents
Network_motif
Graph layout on multiple half-planes
expansion, the subgraph isomorphism problem, of finding whether a pattern graph of bounded size exists as a subgraph of a larger graph, can be solved in linear
Book_embedding
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the
Signal-flow_graph
GRAPH ISOMORPHISM-PROBLEM
GRAPH ISOMORPHISM-PROBLEM
Boy/Male
Arabic, Modern
Grape
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Boy/Male
Biblical
A grape, a knot.
Girl/Female
Indian
Grape like
Boy/Male
Muslim
Grape
Girl/Female
Muslim
Grape like
Biblical
a grape; a knot
Boy/Male
Afghan, Hebrew, Indian, Parsi, Sanskrit
Grape Presser; World; Song
Female
Thai/Siamese
Thai name A-GUN means "grape."
Boy/Male
Indian
Grape
Boy/Male
Biblical
A grape, a knot.
Boy/Male
Hindu, Indian
Efficient; Conqueror of Miseries; Bond in Affection; Capable; Mysterious; Different than Others; Smart; Most Mysterious Vastu Grah 'Rahu'; Son of Lord Buddha; Son of Goddess Durga; Truth Follower; Best of All
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Girl/Female
Indian
Grape vine
Girl/Female
Hindu
Grape, Belonging to kashmir
Boy/Male
African, Arabic
Grape Vines
Girl/Female
Afghan, Arabic, Hebrew, Indian, Muslim, Parsi, Sanskrit
Grape Presser; World; Song; Universe
Girl/Female
Muslim
Grape vine
Girl/Female
Tamil
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Grape, Belonging to kashmir
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Boy/Male
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
GRAPH ISOMORPHISM-PROBLEM
GRAPH ISOMORPHISM-PROBLEM
Boy/Male
Tamil
Feet pad of Lord Vishnu
Boy/Male
Arabic, Muslim
Reviver; Love
Girl/Female
Hindu, Indian, Marathi
Bright Eyed
Boy/Male
Hindu
Young Krishna
Girl/Female
Hebrew, Indian, Punjabi, Sikh
Honey; Happiness; Beautiful Diamond
Boy/Male
Hindu, Indian, Marathi
Gracious; Lord Shiva
Girl/Female
Christian & English(British/American/Australian)
Little Bear
Girl/Female
Hindu, Indian
Effort; Motion
Girl/Female
Tamil
Name of a Raga
Male
Native American
Native American Hopi name CHEVEYO means "spirit warrior."
GRAPH ISOMORPHISM-PROBLEM
GRAPH ISOMORPHISM-PROBLEM
GRAPH ISOMORPHISM-PROBLEM
GRAPH ISOMORPHISM-PROBLEM
GRAPH ISOMORPHISM-PROBLEM
a.
Isomorphous.
a.
Having the quality of isomorphism.
n.
The quality of representing or using animal forms; as, zoomorphism in ornament.
n.
A sort of grape.
n.
Isomorphism between the two forms severally of two dimorphous substances.
a.
Resembling a grape.
n.
The transformation of men into beasts.
n.
A near similarity of crystalline forms between unlike chemical compounds. See Isomorphism.
a.
Having the quality of isodimorphism.
n.
The representation of God, or of gods, in the form, or with the attributes, of the lower animals.
n.
A mangy tumor on the leg of a horse.
n.
A similarity of crystalline form between substances of similar composition, as between the sulphates of barium (BaSO4) and strontium (SrSO4). It is sometimes extended to include similarity of form between substances of unlike composition, which is more properly called homoeomorphism.
n.
Grapeshot.
n.
A seed of the grape.
a.
Of or pertaining to zoomorphism.
n.
Isomorphism between substances that are isomeric.
a.
Composed of, or resembling, grapes.
n.
Isomorphism between the three forms, severally, of two trimorphous substances.