Assertion: graph's complement | /r/HasProperty | perfect
Facets:
Source sentences:
text: The fact that the complement of a perfect graph is also perfect is the perfect graph theorem of László Lovász.
text: Another class of related results concerns perfect graphs: every bipartite graph, the complement of every bipartite graph, the line graph of every bipartite graph, and the complement of the line graph of every bipartite graph, are all perfect.
text: The theory of perfect graphs developed from a 1958 result of Tibor Gallai that in modern language can be interpreted as stating that the complement of a bipartite graph is perfect; this result can also be viewed as a simple equivalent of Kőnig's theorem, a much earlier result relating matchings and vertex covers in bipartite graphs.
text: For instance, Dilworth's theorem states that the minimum number of chains in a partition of a partially ordered set into chains equals the maximum size of an antichain, and can be rephrased as stating that the complements of comparability graphs are perfect.
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.