Perfect Graphs and the Perfect Graph Theorems
نویسنده
چکیده
The theory of perfect graphs relates the concept of graph colorings to the concept of cliques. In this paper, we introduce the concept of a perfect graph as well as a number of graph classes that are always perfect. We next introduce both theWeak Perfect Graph Theorem and the Strong Perfect Graph Theorem and provide a proof of the Weak Perfect Graph Theorem. We also demonstrate an application of perfect graphs, using perfect graphs to prove both Mirsky's Theorem and Dilworth's Theorem.
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