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...

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

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

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

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...

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...

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...

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...

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

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...

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...

In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph G {\displaystyle G} , find the maximal number of edges...

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...

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

have a forbidden graph characterization according to which no induced subgraph can be a house (the complement graph of a five-vertex path graph), hole...

family of graphs, the apex graphs have a forbidden graph characterization. There are only finitely many graphs that are neither apex graphs nor have another...

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...

of 9 forbidden induced subgraphs. (See the article on line graphs.) No characterization by forbidden induced subgraphs is known of line graphs of k-uniform...

string graphs was eventually proven to be NP-complete, implying that no simple characterization is likely to exist. Every planar graph is a string graph: one...

characterization of line graphs (derived graph) in terms of the nine Forbidden graph characterization. Beineke has taught mathematics at Purdue University Fort Wayne...

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

Petersen family, due to the two characterizations of the linklessly embeddable graphs as the graphs with μ ≤ 4 and as the graphs with no Petersen family minor...

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...