Perfect graphs

graph in which all cycles of four or more vertices have a chord

graph whose maximum clique’s size equals the chromatic number

intersection graph of a collection of intervals of the real line

theorem showing that maximum matching and minimum vertex cover are equivalent for bipartite graphs

theorem that the maximum size of an antichain in a finite partial order equals the minimum number of chains into which it can be partitioned

thumb|The Goldner–Harary graph, an example of a planar 3-tree. In graph theory, a '''k-tree' is an undirected graph formed by starting with a (k + 1)-vertex complete graph and then repeatedly adding vertices in such a way that each added vertex v has exactly k neighbors U such that, together, the k + 1 vertices formed by v and U'' form a clique.

thumb|The Turán graph T(13,4) is a cograph In graph theory, a cograph, or complement-reducible graph, or '''P4-free graph', is a graph that can be generated from the single-vertex graph K1 by complementation and disjoint union. That is, the family of cographs is the smallest class of graphs that includes K''1 and is closed under complementation and disjoint union.

graph which partitions into a clique and independent set

graph whose vertices represent the elements of a permutation

graph that can be constructed with a sequence of operations that add either an isolated vertex or a dominating vertex

undirected graph linking pairs of comparable elements in a partial order

undirected graph constucted by joining multiple complete graphs at a shared universal vertex

graph whose line graph is perfect

graph whose induced subgraphs preserve distance

connected graph whose biconnected components are all cliques

theorem in graph theory

perfect graphs have neither odd holes nor odd antiholes

graph that represents all legal moves of the rook chess piece on a chessboard