In graph theory, a trivially perfect graph is a graph with the property that in each of its induced subgraphs the size of the maximum independent set equals...

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...

split graph. Every graph that is both a trivially perfect graph and the complementary graph of a trivially perfect graph is a threshold graph. Threshold...

graph is a forest. More advanced kinds of graphs are: Petersen graph and its generalizations; perfect graphs; cographs; chordal graphs; other graphs with...

permutation graph of a separable permutation. A cograph is a graph all of whose minimal chordal completions are trivially perfect graphs. A cograph is...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

interval graphs that have an interval representation in which every two intervals are either disjoint or nested are the trivially perfect graphs. A graph has...

Threshold graph, a graph whose edges are determined by sums of vertex labels rather than differences of labels Trivially perfect graph, interval graphs for...

1016/0095-8956(74)90063-X, MR 0337679 Golumbic, Martin Charles (1978), "Trivially perfect graphs", Discrete Mathematics, 24 (1): 105–107, doi:10.1016/0012-365X(78)90178-4...

Theorem 1.4.17, pp. 37ff.. Cook et al. (2011). "Trivially", according to Lovász (1974). This is the perfect graph theorem of Lovász (1972) Lovász (1974). Lovász...

results concerns perfect graphs: every bipartite graph, the complement of every bipartite graph, the line graph of every bipartite graph, and the complement...

In graph theory, the perfect graph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph...

proper interval graphs. And G is a cograph if and only if all of its minimal chordal completions are trivially perfect graphs. A graph G has treewidth...

even-hole-free graphs are the graphs containing no induced cycles with an even number of vertices. The trivially perfect graphs are the graphs that have neither...

distance-hereditary graphs known as the trivially perfect graphs, which are also called chordal cographs. Distance-hereditary graphs can be recognized,...

the sense of graph theory in one of two ways: either as a tree (graph theory) or as a trivially perfect graph. In the first case, the graph is the undirected...

logic of graphs, and for apex graphs. Graphs that contain a universal vertex include the stars, trivially perfect graphs, and friendship graphs. For wheel...

complement of a graph hole. Chordless cycles may be used to characterize perfect graphs: by the strong perfect graph theorem, a graph is perfect if and only...

{\displaystyle F} forms a trivially perfect graph, and the height of F {\displaystyle F} is the size of the largest clique in this graph. Thus, the tree-depth...

Therefore, permutation graphs are another subclass of comparability graphs. The trivially perfect graphs are the comparability graphs of rooted trees. Cographs...

complete graphs from which it is formed, it is (k − 1)-edge-connected. It is trivially perfect and a block graph. By construction, the windmill graph Wd(3...

By convention, graphs which satisfy the definition trivially are excluded from detailed studies and lists of strongly regular graphs. These include the...

In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander...

In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph...

planar graph. The set of all pairs of vertices in this tree-decomposition that both belong to a common node of the tree-decomposition forms a trivially perfect...

In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a...

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability...

in a Turán graph lead to notable graphs that have been independently studied. The Turán graph T(2n,n) can be formed by removing a perfect matching from...

In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly...

computer science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph isomorphism problem is...