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Perfect graphs

Last update: 15 Dec 2020  | Contains: 146748 graphs

A perfect graph is a simple graph such that for every induced subgraph, its clique number equals its chromatic number. A graph is also perfect if and only if neither the graph nor its complement graph has a chordless cycle of odd order, where a chord is an edge that is not part of the cycle but connects two vertices of the cycle. The following collection was calculated by Brendan McKay (source) and lists all perfect graphs up to 9 vertices. Graphs of order 4 or less were included from the Eric Weisstein's MathWorld (source).

OEIS: A052431

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