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...

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...

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...

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...

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

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges...

induced cycle in the graph should have exactly three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings...

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...

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...

bipartite graph, can be interpreted as stating that the line graph of a bipartite graph is perfect. Since line graphs of bipartite graphs are perfect, the...

In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. More formally, given a graph G with edges E and vertices...

the complement of a perfect graph is also perfect is the perfect graph theorem of László Lovász. Cographs are defined as the graphs that can be built up...

Meyniel graphs are a subclass of the perfect graphs. Every induced subgraph of a Meyniel graph is another Meyniel graph, and in every Meyniel graph the size...

In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain...

intersection graph of the intervals. Interval graphs are chordal graphs and perfect graphs. They can be recognized in linear time, and an optimal graph coloring...

special cases of the distance-hereditary graphs, permutation graphs, comparability graphs, and perfect graphs. Any cograph may be constructed using the...

In graph theory, a line perfect graph is a graph whose line graph is a perfect graph. Equivalently, these are the graphs in which every odd-length simple...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability...

component of a decomposition of perfect graphs used to prove the strong perfect graph theorem, which characterizes all perfect graphs. The independence number...

characterization of claw-free perfect graphs. They are the subject of hundreds of mathematical research papers and several surveys. The line graph L ( G ) {\displaystyle...

two-vertex complete graph, and may be decomposed into two copies of Qn − 1 connected to each other by a perfect matching. Hypercube graphs should not be confused...

cover. A perfect graph is a graph in which the clique number equals the chromatic number in every induced subgraph. A split graph is a graph in which...

Because chordal graphs are perfect, so are the split graphs. The double split graphs, a family of graphs derived from split graphs by doubling every...

Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De...

three graphs. A perfect matching is a matching that matches all vertices of the graph. That is, a matching is perfect if every vertex of the graph is incident...

In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations...

In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to...

the given graph. Perfectly orderable graphs form a special case of the perfect graphs, and they include the chordal graphs, comparability graphs, and distance-hereditary...

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