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SUPERGRAPH

Supergraph

Topics referred to by the same term

and physics, the word supergraph has several meanings: In graph theory, if A is a subgraph of B, then B is said to be a supergraph of A. In the context

Supergraph

Glossary of graph theory

completion of a given graph is a supergraph that has some desired property. For instance, a chordal completion is a supergraph that is a chordal graph. 3. A

Glossary of graph theory

Glossary_of_graph_theory

Unit distance graph

Geometric graph with unit edge lengths

{\displaystyle G} is not a non-strict unit distance graph, neither is any supergraph H {\displaystyle H} of G {\displaystyle G} . A similar idea works for

Unit distance graph

Unit_distance_graph

Tree-depth

Numerical invariant of graphs

invariant of G {\displaystyle G} , the minimum height of a Trémaux tree for a supergraph of G {\displaystyle G} . This invariant and its close relatives have gone

Tree-depth

Epigraph (mathematics)

Region above a graph

In mathematics, the epigraph or supergraph of a function f : X → [ − ∞ , ∞ ] {\displaystyle f:X\to [-\infty ,\infty ]} valued in the extended real numbers

Epigraph (mathematics)

Epigraph_(mathematics)

Hoffman–Singleton graph

7-regular undirected graph with 50 nodes and 175 edges

Singleton graph is contained in the Higman–Sims graph which is therefore a supergraph. McKay–Miller–Širáň graphs, a class of graphs including the Hoffman–Singleton

Hoffman–Singleton graph

Hoffman–Singleton_graph

Euclidean minimum spanning tree

Shortest network connecting points

A Euclidean minimum spanning tree of a finite set of points in the Euclidean plane or higher-dimensional Euclidean space connects the points by a system

Euclidean minimum spanning tree

Euclidean_minimum_spanning_tree

Graph bandwidth

Node labeling problem in graph theory

defined as one less than the maximum clique size in a proper interval supergraph of the given graph, chosen to minimize its clique size. For several families

Graph bandwidth

Graph_bandwidth

Pathwidth

Representation of a graph as a path graph "thickened" by some amount

interval thickness (one less than the maximum clique size in an interval supergraph of G), vertex separation number, or node searching number. Pathwidth and

Pathwidth

Graph sandwich problem

graphs, one of which must be a subgraph and the other of which must be a supergraph of the desired graph. Graph sandwich problems generalize the problem of

Graph sandwich problem

Graph_sandwich_problem

Triangulation (disambiguation)

Topics referred to by the same term

1999 novel by Phil Whitaker Plane triangulation, and a maximal planar supergraph of a graph G may be called a triangulation of G Triangulated graph, and

Triangulation (disambiguation)

Triangulation_(disambiguation)

Clebsch graph

One of two different regular graphs with 16 vertices

and every four-chromatic induced subgraph of the Clebsch graph is a supergraph of the Grötzsch graph. More strongly, every triangle-free four-chromatic

Clebsch graph

Clebsch_graph

Semi-Yao graph

{\displaystyle \theta } and an appropriate cone axis, the k-SYG gives a supergraph of the k-nearest neighbor graph (k-NNG). For example, in 2D, if we partition

Semi-Yao graph

Semi-Yao_graph

Interval graph

Intersection graph for intervals on the real number line

subgraph. The parameterized version of interval completion (find an interval supergraph with k additional edges) is fixed parameter tractable, and moreover, is

Interval graph

Interval_graph

Supersymmetry nonrenormalization theorems

Martin Rocek and Warren Siegel in their 1979 paper Improved methods for supergraphs. Nonrenormalization theorems in supersymmetric theories are often consequences

Supersymmetry nonrenormalization theorems

Supersymmetry_nonrenormalization_theorems

Clique problem

Task of computing complete subgraphs

meaning that, if a clique exists in a given graph, it will exist in any supergraph. Because this property is monotone, there must exist a monotone circuit

Clique problem

Clique_problem

Nested triangles graph

Planar graph used as counterexample

layout uses less area than Frati & Patrignani (2008) but unlike theirs does not generalize to maximal planar supergraphs of the nested triangles graph.

Nested triangles graph

Nested_triangles_graph

Dense subgraph

Highly connected subgraph

density in its local region in the graph: it is neither contained in any supergraph with the same or larger density, nor it contains subgraphs with density

Dense subgraph

Dense_subgraph

Aanderaa–Karp–Rosenberg conjecture

Unsolved problem on graph query complexity

every supergraph of this graph on the same vertex set also possesses it. For instance, the property of being nonplanar is monotone: a supergraph of a nonplanar

Aanderaa–Karp–Rosenberg conjecture

Aanderaa–Karp–Rosenberg_conjecture

Georg Glaeser

Austrian mathematician

Teubner, 1986. Objektorientiertes Graphik-Programmieren mit der Pascal Unit Supergraph. Teubner, 1992. Amiga 3D-Sprinter. Pearson Education, 1993. Glaeser, Georg

Georg Glaeser

Georg_Glaeser

De Bruijn–Erdős theorem (graph theory)

On coloring infinite graphs

-coloring of G {\displaystyle G} in which each finite graph has a larger supergraph whose coloring agrees with the coloring of the whole graph. If a graph

De Bruijn–Erdős theorem (graph theory)

De_Bruijn–Erdős_theorem_(graph_theory)

Kinetic closest pair

Kinetic data structure

Delaunay triangulations, so called Equilateral Delaunay graph (EDG), is a supergraph for the nearest neighbor graph (NNG); the endpoints of the edge with minimum

Kinetic closest pair

Kinetic_closest_pair

Halin graph

Mathematical tree with cycle through leaves

ISBN 978-3540194880. Horton, S. B.; Parker, R. Gary (1995), "On Halin subgraphs and supergraphs", Discrete Applied Mathematics, 56 (1): 19–35, doi:10.1016/0166-218X(93)E0131-H

Halin graph

Halin_graph

Hereditary property

Property of objects inherited by all their subobjects

addition of edges and vertices (i.e., the property should hold for all supergraphs). Preserved by the addition of edges. (This meaning is used in the statement

Hereditary property

Hereditary_property

Chordal completion

Chordal graph with the given graph as a subgraph

Eppstein, David (November 15, 2012), Graph parameters and cliques in supergraphs. Rose, Donald J. (1972), "A graph-theoretic study of the numerical solution

Chordal completion

Chordal_completion

Warren Siegel

American quantum physicist

Grisaru, Siegel and Rocek in their 1979 paper "Improved methods for Supergraphs", which has close to 700 citations. During the 1980s, Siegel invented

Warren Siegel

Warren_Siegel

Network motif

Type of sub-graph

generalize a mapping of a k-size graph into the network to its same size supergraphs. For example, suppose there is mapping f(G) of graph G with k nodes into

Network motif

Network_motif

Index of physics articles (S)

Superfluid film Superfluid helium-4 Superfluid vacuum Superghost Superglass Supergraph Supergravity Supergroup (physics) Superheating Superhydrophobe Superinsulator

Index of physics articles (S)

Index_of_physics_articles_(S)