Abstract
AbstractThe Erdős–Lovász Tihany conjecture asserts that every graph G with ) contains two vertex disjoint subgraphs G1 and G2 such that and . Under the same assumption on G, we show that there are two vertex disjoint subgraphs G1 and G2 of G such that (a) and or (b) and . Here, is the chromatic number of is the clique number of G, and col(G) is the coloring number of G.
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