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A. Davoodi

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Preprint Sep 2026

Local Clique Covers and Chromatic Number

The local clique cover number $lcc(G)$ is the minimum valency of an edge-clique cover of $G$. We prove the conjectured inequality $lcc(G)+\chi(G)\le |V(G)|+1$ for every finite simple graph. The proof gives an independent set improvement of an endpoint-cover estimate and applies the resulting construction to an induced...

A. Davoodi · 0 citations