Graph where every connected induced subgraph has a universal vertex
Construction of a trivially perfect graph from nested intervals and from the reachability relationship in a tree
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 the number of maximal cliques.[1] Trivially perfect graphs were first studied by (Wolk 1962, 1965) but were named by Golumbic (1978); Golumbic writes that "the name was chosen since it is trivial to show that such a graph is perfect." Trivially perfect graphs are also known as comparability graphs of trees,[2]arborescent comparability graphs,[3] and quasi-threshold graphs.[4]
^Brandstädt, Le & Spinrad (1999), definition 2.6.2, p.34; Golumbic (1978).
^Wolk (1962); Wolk (1965).
^Donnelly & Isaak (1999).
^Yan, Chen & Chang (1996).
and 23 Related for: Trivially perfect graph information
In graph theory, a triviallyperfectgraph 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 perfectgraph 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 triviallyperfectgraph and the complementary graph of a triviallyperfectgraph is a threshold graph. Threshold...
In graph theory, the perfectgraph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph...
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...
results concerns perfectgraphs: every bipartite graph, the complement of every bipartite graph, the line graph of every bipartite graph, and the complement...
interval graphs that have an interval representation in which every two intervals are either disjoint or nested are the triviallyperfectgraphs. A graph has...
Therefore, permutation graphs are another subclass of comparability graphs. The triviallyperfectgraphs are the comparability graphs of rooted trees. Cographs...
even-hole-free graphs are the graphs containing no induced cycles with an even number of vertices. The triviallyperfectgraphs are the graphs that have neither...
permutation graph of a separable permutation. A cograph is a graph all of whose minimal chordal completions are triviallyperfectgraphs. A cograph is...
Threshold graph, a graph whose edges are determined by sums of vertex labels rather than differences of labels Triviallyperfectgraph, interval graphs for...
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...
By convention, graphs which satisfy the definition trivially are excluded from detailed studies and lists of strongly regular graphs. These include the...
complete graphs from which it is formed, it is (k – 1)-edge-connected. It is triviallyperfect and a block graph. By construction, the windmill graph Wd(3...
proper interval graphs. And G is a cograph if and only if all of its minimal chordal completions are triviallyperfectgraphs. A graph G has treewidth...
The wheel graphs, similarly, may be formed by adding a universal vertex to a cycle graph. The triviallyperfectgraphs (the comparability graphs of order-theoretic...
computer science: Can the graph isomorphism problem be solved in polynomial time? (more unsolved problems in computer science) The graph isomorphism problem...
connection with perfectgraphs. Chvátal proved that a minimally imperfect graph could not have a star cutset. Trivially, disconnected graphs cannot be minimally...
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability...
determine the graph. The conjecture has been verified for a number of infinite classes of graphs (and, trivially, their complements). Regular graphs - Regular...
k} -regular graph with 2 n {\displaystyle 2n} vertices is 1-factorable. The perfect 1-factorization conjecture that every complete graph on an even number...
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander...
Global Information