The perfect graph theorem, proved by Laszlo Lovasz in 1972, states that an undirected graph is perfect if and only if its complement is also perfect, confirming a conjecture Claude Berge had made in the early 1960s. A perfect graph is one in which the size of the largest clique equals the minimum number of colors needed to color every induced subgraph, a class including bipartite graphs, chordal graphs and comparability graphs; the theorem is sometimes called the weak perfect graph theorem to distinguish it from the strong perfect graph theorem, which characterizes perfect graphs by forbidden induced subgraphs. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Source Perfect graph theorem (Wikipedia)
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1. Perfect graph theorem (Wikipedia)
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In graph theory, the perfect graph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph is also perfect.
- In Branch: Graph Theory, Lead sentence
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