Assertion: graph | /r/HasProperty | perfect
Facets:
value: by the strong perfect graph theorem
type: OTHER
Source sentences:
text: Chordless cycles may be used to characterize perfect graphs: by the strong perfect graph theorem, a graph is perfect if and only if none of its holes or antiholes have an odd number of vertices that is greater than three.
text: According to the strong perfect graph theorem, the perfect graphs have a forbidden graph characterization resembling that of bipartite graphs: a graph is bipartite if and only if it has no odd cycle as a subgraph, and a graph is perfect if and only if it has no odd cycle or its complement as an induced subgraph.
text: The first of these two theorems was the perfect graph theorem of Lovász (1972), stating that a graph is perfect if and only if its complement is perfect.
text: It states that a graph is perfect if the sizes of the largest clique, and the largest independent set, when multiplied together, equal or exceed the number of vertices of the graph, and the same is true for any induced subgraph.