Abstract:Resolving in a strong sense a problem of Gyárfás on the union of two perfect graphs, we prove that for every pair of positive integers $d$ and $k$, there is a graph $G$ with clique number $k$ and chromatic number $k^d$ that is the union of $d$ comparability graphs. We also show that the chromatic number can be replaced by the fractional chromatic number or $\frac{|V(G)|}{\alpha(G)}$.
From: Seokbeom Kim [view email]
[v1]
Mon, 8 Jun 2026 12:29:23 UTC (6 KB)
[v2]
Mon, 3 Aug 2026 01:31:55 UTC (10 KB)
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