these two graphs as a subgraph (in which case it does not belong to the planar graphs). More generally, a forbidden graph characterization is a method...

In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states...

In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither...

families of graphs defined by forbidden graph characterization have either large cliques or large cocliques. Several important classes of graphs may be defined...

In graph theory, Wagner's theorem is a mathematical forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite...

forbidden A forbidden graph characterization is a characterization of a family of graphs as being the graphs that do not have certain other graphs as...

belonging to the same to cliques, and the characterization by forbidden graphs has seven forbidden graphs instead of nine. However, for multigraphs,...

strong perfect graph theorem, the perfect graphs have a forbidden graph characterization resembling that of bipartite graphs: a graph is bipartite if...

linklessly embeddable graphs have the Petersen family graphs as their forbidden minors, and include the planar graphs and apex graphs. They may be recognized...

bounded face of a maximal outerplanar graph is a triangle. Outerplanar graphs have a forbidden graph characterization analogous to Kuratowski's theorem and...

In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every...

form a forbidden graph characterization of F {\displaystyle {\mathcal {F}}} : the graphs in F {\displaystyle {\mathcal {F}}} are exactly the graphs that...

fixed graph H, it is possible to test whether H is a minor of an input graph G in polynomial time; together with the forbidden minor characterization this...

Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Holt graph Horton...

Kuratowski provided a characterization of planar graphs in terms of forbidden graphs, now known as Kuratowski's theorem: A finite graph is planar if and only...

the graph with the property that any single cycle is unknotted. The graphs that have linkless embeddings have a forbidden graph characterization involving...

are always equal. They also have a forbidden graph characterization as the graphs that do not have the diamond graph or a cycle of four or more vertices...

; Makhnev, A. A.; Paduchikh, D. V. (2007), "Characterization of some distance-regular graphs by forbidden subgraphs", Doklady Akademii Nauk, 414 (5):...

for being independent. Threshold graphs also have a forbidden graph characterization: A graph is a threshold graph if and only if it no four of its vertices...

tree-depth of a graph, and as part of the left-right planarity test for testing whether a graph is a planar graph. A characterization of Trémaux trees...

for the other direction of the characterization, based on Wagner's theorem characterizing the planar graphs by forbidden minors. As O'Neill observes, the...

In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique...

strong perfect graph theorem characterizing perfect graphs by their forbidden induced subgraphs. A perfect graph is an undirected graph with the property...

set of forbidden minors consists of the seven graphs in the Petersen family, due to the two characterizations of the linklessly embeddable graphs as the...

such as graph density, toughness, forbidden subgraphs and distance among other parameters. Dirac and Ore's theorems basically state that a graph is Hamiltonian...

mathematical field of graph theory, a prism graph is a graph that has one of the prisms as its skeleton. The individual graphs may be named after the...

In mathematics, and, in particular, in graph theory, a rooted graph is a graph in which one vertex has been distinguished as the root. Both directed and...

series–parallel graph. Wagner's theorem, which characterizes the planar graphs by their forbidden minors, implies that the planar graphs have Hadwiger number...

bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the...

cochromatic graphs, analogous to the definition of perfect graphs via graph coloring, and provides a forbidden subgraph characterization of these graphs. Fomin...