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...

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...

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...

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

mathematics of graphs through their alternative constructions: rook's graphs are the Cartesian product of two complete graphs, and are the line graphs of complete...

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...

the line graph of a bipartite graph is perfect. Since line graphs of bipartite graphs are perfect, the complements of line graphs of bipartite graphs are...

directed graph with no directed cycles Forest, a cycle-free graph Line perfect graph, a graph in which every odd cycle is a triangle Perfect graph, a graph with...

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...

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...

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...

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...

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

subclasses of the perfect graphs, block graphs are perfect. Every tree, cluster graph, or windmill graph is a block graph. Every block graph has boxicity at...

reversed by the permutation. Permutation graphs may also be defined geometrically, as the intersection graphs of line segments whose endpoints lie on two parallel...

same parity, and the line perfect graphs, a generalization of the bipartite graphs. Every parity graph is a Meyniel graph, a graph in which every odd cycle...

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...

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...

key building blocks of line perfect graphs. The term "book-graph" has been employed for other uses. Barioli used it to mean a graph composed of a 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...

These graphs do not fall into many known families of well-structured graphs: they might not be perfect graphs, circle graphs, or chordal graphs. An exception...

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...

of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are...

points on the bottom line. A graph is a trapezoid graph if there exists a set of trapezoids corresponding to the vertices of the graph such that two vertices...

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

In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an...

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, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting...