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Broken-cycle-free subgraphs and the log-concavity conjecture for chromatic polynomials. (English) Zbl 1120.05032

The authors consider a computational verification of the strict log-concavity conjecture for chromatic polynomials for all graphs on at most 11 vertices and for certain cubic graphs. The (heuristic) behavior of the coefficients of the chromatic polynomial under edge deletion and contraction are studied. Some problems and conjectures are given, too.

MSC:

05C15 Coloring of graphs and hypergraphs
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