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theoretical computer science, a maximum common induced subgraph of two graphs G and H is a graph that is an induced subgraph of both G and H, and that has
Maximum common induced subgraph
Maximum_common_induced_subgraph
Index of articles associated with the same name
computer science, a maximum common subgraph may mean either: Maximum common induced subgraph, a graph that is an induced subgraph of two given graphs
Maximum_common_subgraph
graphs G {\displaystyle G} and G ′ {\displaystyle G'} , the maximum common edge subgraph problem (or MCES problem) is the problem of finding a graph H
Maximum_common_edge_subgraph
Task of computing complete subgraphs
reduce the problem of finding the maximum common induced subgraph of two graphs to the problem of finding a maximum clique in their product. In automatic
Clique_problem
Binary operation in graph theory
cliques in graphs. Specifically, the maximum common induced subgraph of both G and H corresponds to the maximum clique in their modular product. Although
Modular_product_of_graphs
Graph representing edges of another graph
sharing a common edge). Every line perfect graph is itself perfect. All line graphs are claw-free graphs, graphs without an induced subgraph in the form
Line_graph
Problem in theoretical computer science
{\displaystyle G} contains a subgraph that is isomorphic to H {\displaystyle H} . Subgraph isomorphism is a generalization of both the maximum clique problem and
Subgraph_isomorphism_problem
Problem in graph theory
cycle transversal, equivalent to asking for the largest bipartite induced subgraph Unfriendly partition, a related concept for infinite graphs Edwards (1973
Maximum_cut
other graphs as subgraphs, induced subgraphs, or minors. If H is one of the graphs that does not occur as a subgraph, induced subgraph, or minor, then
Glossary_of_graph_theory
Set of edges without common vertices
the graph is called factor-critical. An induced matching is a matching that is the edge set of an induced subgraph. Given a matching M, an alternating path
Matching_(graph_theory)
Area of discrete mathematics
problem is finding induced subgraphs in a given graph. Again, some important graph properties are hereditary with respect to induced subgraphs, which means
Graph_theory
Statement in mathematical combinatorics
for induced subgraphs. Roughly speaking, instead of finding a monochromatic subgraph, we are now required to find a monochromatic induced subgraph. In
Ramsey's_theorem
Graph formed by complementation and disjoint union
nontrivial induced subgraph has at least two vertices with the same neighbourhoods. A cograph is a graph in which every nontrivial connected induced subgraph has
Cograph
Tree node with two other nodes as descendants
definition, where the lowest common ancestors of x and y are the nodes of out-degree zero in the subgraph of G induced by the set of common ancestors of x and y
Lowest_common_ancestor
Graph of short distances in another graph
graph is squared. The half-square of a bipartite graph G is the subgraph of G2 induced by one side of the bipartition of G. Map graphs are the half-squares
Graph_power
(especially with weighted edges) maximum cut. Maximum common subgraph isomorphism problem Maximum independent set Maximum Induced path Minimum maximal independent
List_of_NP-complete_problems
Graph with tight clique-coloring relation
chromatic number equals the size of the maximum clique, both in the graph itself and in every induced subgraph. In all graphs, the chromatic number is
Perfect_graph
Geometric graph with unit edge lengths
hereditary family of graphs, they can be characterized by forbidden induced subgraphs. The unit distance graphs include the cactus graphs, the matchstick
Unit_distance_graph
Subgraph with contracted edges
called an induced minor of a graph G if it can be obtained from an induced subgraph of G by contracting edges. Otherwise, G is said to be H-induced minor-free
Graph_minor
Methodic assignment of colors to elements of a graph
removes them from the graph. These actions are repeated on the remaining subgraph until no vertices remain. The worst-case complexity of DSatur is O ( n
Graph_coloring
Largest independent set of paired elements
matroid parity algorithms include finding large planar subgraphs and finding graph embeddings of maximum genus. Matroid parity algorithms can also be used
Matroid_parity_problem
Graph of chess rook moves
the maximum number of squares from the subset in any single row or column (the clique number of the induced subgraph). This class of induced subgraphs are
Rook's_graph
Graph divided into two independent sets
has no odd cycle as a subgraph, and a graph is perfect if and only if it has no odd cycle or its complement as an induced subgraph. The bipartite graphs
Bipartite_graph
Intersection graph of unit disks in the plane
contain an induced K 1 , 6 {\displaystyle K_{1,6}} subgraph. Infinitely many other forbidden induced subgraphs are known. The number of unit disk graphs on
Unit_disk_graph
Unsolved problem in extremal graph theory
graph that has a given number of vertices and has no complete bipartite subgraphs of a given size? More unsolved problems in mathematics The Zarankiewicz
Zarankiewicz_problem
Graph where all long cycles have a chord
A\cup S} and S ∪ B {\displaystyle S\cup B} both form chordal induced subgraphs, S is a clique, and there are no edges from A to B. That is, they
Chordal_graph
Graph whose biconnected components are all cliques
not have the diamond graph or a cycle of four or more vertices as an induced subgraph; that is, they are the diamond-free chordal graphs. They are also the
Block_graph
Type of sub-graph
can be used for directed or undirected networks as well as induced or non-induced subgraphs.[citation needed] Kashtan et al. published mfinder, the first
Network_motif
Partition of the vertices of a graph
common to identify the sets A ( G ) {\displaystyle A(G)} , C ( G ) {\displaystyle C(G)} , and D ( G ) {\displaystyle D(G)} with the subgraphs induced
Gallai–Edmonds_decomposition
Data mining for patterns in molecule data
Detector (SMSD)- is a Java-based software library for calculating Maximum Common Subgraph (MCS) between small molecules. This will help us to find similarity/distance
Molecule_mining
Directed graph with no directed cycles
two vertices. Equivalently, it is a DAG in which the subgraph reachable from any vertex induces an undirected tree. A polytree (also called a directed
Directed_acyclic_graph
Graph with sign-labeled edges
Cut. The third question is called the Frustration Number or Maximum Balanced Induced Subgraph problem, is also NP-hard; see e.g. There are two matroids
Signed_graph
conjecture on large cliques or independent sets in graphs with a forbidden induced subgraph The Grünbaum–Nash-Williams conjecture on whether every 4-vertex-connected
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
On bipartite matching and vertex cover
case of maximum flow, the theorem also results from the max-flow min-cut theorem. A graph is said to be perfect if, in every induced subgraph, the chromatic
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
On chains and antichains in partial orders
independent set in a comparability graph corresponds to an antichain. Any induced subgraph of a comparability graph is itself a comparability graph, formed from
Dilworth's_theorem
Number denoting a graph's closeness to a tree
the smallest hitting set for the family of subgraphs, and the treewidth of a graph is one less than the maximum order of a bramble. Every complete graph
Treewidth
Intersection graph representing regions on the Euclidean plane
most two steps apart in G. The half-square or bipartite half is the induced subgraph of one side of the bipartition (say V) in the square graph: its vertex
Map_graph
Graph obeys some properties of random graphs
among U {\displaystyle U} (equivalently, the number of edges in the subgraph induced by the vertex set U {\displaystyle U} ). It can be shown that the Erdős–Rényi
Pseudorandom_graph
strong component algorithm Tarjan's strongly connected components algorithm Subgraph isomorphism problem Bitap algorithm: fuzzy algorithm that determines if
List_of_algorithms
Operation in graph theory
defined by replacing the subgraph of G {\displaystyle G} induced by N G ( v ) {\displaystyle N_{G}(v)} with its complementary subgraph. In other words, two
Local_complementation
Graph partition into regular subgraphs
prove Szemerédi's theorem. The graph removal lemma generalizes to induced subgraphs, by considering edge edits instead of only edge deletions. This was
Szemerédi_regularity_lemma
Any planar graph can be subdivided by removing a few vertices
partitions a graph G {\displaystyle G} into two subgraphs of equal size, when G {\displaystyle G} is an induced subgraph of a grid graph with no holes or with a
Planar_separator_theorem
Set system used in greedy optimization
and the feasible sets be the vertex subsets containing r that induce connected subgraphs of G. This is called the vertex search greedoid and is a kind
Greedoid
Graph with equal-size maximal independent sets
construction when p consists of n one-vertex cliques. Thus, every graph is an induced subgraph of a well-covered graph. Favaron (1982) defines a very well covered
Well-covered_graph
Representation of a graph as a path graph "thickened" by some amount
taken as the induced subgraphs of the sets Xi in the first definition of path decompositions, with two vertices in successive induced subgraphs being glued
Pathwidth
Shortest network connecting points
regions can be used to prove that the Euclidean minimum spanning tree is a subgraph of other geometric graphs including the relative neighborhood graph and
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Mixing property of Markov chains and graphs
in a graph) should be low. Apart from this, the conductance of the subgraph induced by a cluster (called "internal conductance") can be used as well. For
Conductance_(graph_theory)
Since the graph of the instance they produce is a subgraph of the induced graph, if the induced width is bounded by a constant the generated instance
Local_consistency
Abstraction of linear independence of vectors
number of the subgraph induced on the edge subset F {\displaystyle F} , which equals the number of edges outside a maximal forest of that subgraph, and also
Matroid
Technique in graph theory
P_{3}} . Denoting d ( H , G ) {\displaystyle d(H,G)} as the induced density of a subgraph H {\displaystyle H} in G {\displaystyle G} , double counting
Flag_algebra
Solid with twenty equal triangular faces
the central of all of those three, and the icosahedral graph has no induced subgraph, a claw-free graph. The icosahedral graph is a graceful graph, meaning
Regular_icosahedron
Generalization of graph theory
connected hypergraph H is a host graph for H if every hyperedge of H induces a connected subgraph in G. For a disconnected hypergraph H, G is a host graph if there
Hypergraph
Mathematical object
The clique complex of G is an ASC whose faces are all cliques (complete subgraphs) of G. The independence complex of G is an ASC whose faces are all independent
Abstract_simplicial_complex
Graph layout on multiple half-planes
thickness. The same is true for detecting whether the pattern graph is an induced subgraph of the larger graph, or whether it has a graph homomorphism to the
Book_embedding
Network whose degree distribution follows a power law
nodes and power-law exponent γ > 3 {\displaystyle \gamma >3} , the induced subgraph constructed by vertices with degrees larger than log n × log ∗
Scale-free_network
Graph whose vertices correspond to combinations of a set of n elements
Ellis, David; Friedgut, Ehud; Lifshitz, Noam (2025), "On the maximum degree of induced subgraphs of the Kneser graph", Combinatorial Theory, 5 (1), Paper#16
Kneser_graph
{\displaystyle T} , the graphs that do not contain T {\displaystyle T} as an induced subgraph are χ {\displaystyle \chi } -bounded. For instance, this would include
Chi-bounded
Social structure made up of a set of social actors
network ties. Parameters are given in terms of the prevalence of small subgraph configurations in the network and can be interpreted as describing the
Social_network
Settlement without third party involvement
related to the edge expansion of the graph. Well-connected "communities" (subgraphs with high edge expansion) exhibit high liquidity among their members,
Collaborative_finance
Threshold of percolation theory models
, such that infinite connectivity (percolation) first occurs. The most common percolation model is to take a regular lattice, like a square lattice, and
Percolation_threshold
Predictive chemical model
substructures. Furthermore, there exist also approaches using maximum common subgraph searches or graph kernels. Typically QSAR models derived from non
Quantitative structure–activity relationship
Quantitative_structure–activity_relationship
random graphs, including distribution of components, occurrence of small subgraphs, and phase transitions. L. R. Ford, Jr. & D. R. Fulkerson Flows in Networks
List of publications in mathematics
List_of_publications_in_mathematics
{\displaystyle S_{i}} of coclass r {\displaystyle r} (Theorem D) and a finite subgraph G 0 ( p , r ) {\displaystyle {\mathcal {G}}_{0}(p,r)} of sporadic groups
Descendant tree (group theory)
Descendant_tree_(group_theory)
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MAXIMUM COMMON-INDUCED-SUBGRAPH
MAXIMUM COMMON-INDUCED-SUBGRAPH
Male
Russian
(МакÑим) Variant spelling of Russian Maksim, MAXIM means "the greatest." Compare with another form of Maxim.
Male
Greek
(Ἄμμων) Greek form of Egyptian Yamanu, AMMON means "the hidden one." In mythology, Yamanu is the name of a god of wind and air. Compare with another form of Ammon.
Male
French
French form of Latin Maximus, MAXIME means "the greatest."Â
Male
English
English masculine variant spelling of Scottish Cameron, CAMRON means "crooked nose."
Boy/Male
Latin
Greatest.
Surname or Lastname
Swedish (common in Finland)
Swedish (common in Finland) : ornamental name formed with the common surname suffix -in and an unexplained first element.German : unexplained.English : unexplained.Spanish (FarÃn) : unexplained.
Surname or Lastname
English
English : habitational name from any of the numerous places throughout England (but especially in the south) named Compton, from Old English cumb ‘short, straight valley’ + tūn ‘enclosure’, ‘settlement’.
Male
Romanian
Romanian form of Greek Kosmos, COSMIN means "order, beauty."
Male
Irish
Irish name COMYN means "shrewd."
Male
English
 Anglicized form of Hebrew Ammown, AMMON means "kindred, tribal." In the bible, this is the name of a son of Lot by his younger daughter. Compare with another form of Ammon.
Male
English
 Anglicized form of Hebrew Rimmown, RIMMON means "pomegranate." In the bible, this is the name of several places, the name of a Benjamite of Beeroth.Â
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi
Eashwar
Boy/Male
Latin
Greatest.
Surname or Lastname
English
English : probably from a variant of the personal name Clement.Perhaps a reduced form of Scottish and northern Irish McClymont.
Male
English
English form of Irish Colmán, COLMAN means "dove."
Surname or Lastname
English
English : habitational name from any of numerous places named from Old English cotum (dative plural of cot) ‘at the cottages or huts’ (or sometimes possibly from a Middle English plural, coten). Examples include Coton (Cambridgeshire, Northamptonshire, Staffordshire), Cottam (East Yorkshire, Lancashire, Nottinghamshire), and Cotham (Nottinghamshire).French : from a diminutive of Old French cot(t)e ‘coat (of mail)’ (see Cott).John Cotton (1584–1652) was a noted Puritan preacher, who landed at Boston, MA, from London in 1633 and became leader of the Congregationalists in America.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sanskrit
Plenty; Maximum; Intelligent; Young and Dynamic; Earth
Boy/Male
American, Australian, Chinese, French, German, Greek, Latin, Swedish
Greatest
Surname or Lastname
Scottish and northern Irish
Scottish and northern Irish : variant of Curzon.English (of Norman origin) : nickname from Old French corson, a diminutive of curt ‘short’ (see Court).
Male
Irish
Contracted form of Irish Gaelic Comhghán, COMGAN means "born together."
MAXIMUM COMMON-INDUCED-SUBGRAPH
MAXIMUM COMMON-INDUCED-SUBGRAPH
MAXIMUM COMMON-INDUCED-SUBGRAPH
MAXIMUM COMMON-INDUCED-SUBGRAPH
MAXIMUM COMMON-INDUCED-SUBGRAPH
MAXIMUM COMMON-INDUCED-SUBGRAPH
MAXIMUM COMMON-INDUCED-SUBGRAPH
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