Perfect graph

The Paley graph of order 9, colored with three colors and showing a clique of three vertices. In this graph and each of its induced subgraphs the chromatic number equals the clique number, so it is a perfect graph.

A seven-vertex cycle and its complement, showing in each case an optimal coloring and a maximum clique (shown with heavy edges). Since neither graph uses a number of colors equal to its clique size, neither is perfect.

In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. Due to the strong perfect graph theorem, perfect graphs are the same as Berge graphs. A graph G is a Berge graph if neither G nor its complement has an odd-length induced cycle of length 5 or more.

单词	Perfect graph
释义	Perfect graph 英语百科 Perfect graph In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. Due to the strong perfect graph theorem, perfect graphs are the same as Berge graphs. A graph G is a Berge graph if neither G nor its complement has an odd-length induced cycle of length 5 or more.
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