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Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
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Combinatorial Proof of Weak Perfect Graph Theorem.
I am reading Andras Frank's Connections in Combinatorial Optimization. On the Page 34, the description of how to use the Replication Lemma to prove the weak perfect graph theorem seems only to prove t …