On bounding the difference between the maximum degree and the chromatic number
نویسندگان
چکیده
For every k ∈ N0, we consider graphs in which for any induced subgraph, ∆ ≤ χ − 1 + k holds, and call this family of graphs Υk, where ∆ is the maximum degree and χ is the chromatic number of the subgraph. We give a finite forbidden induced subgraph characterization for every k. The results are compared to those given in [6], where the graphs in which for any induced subgraph, ∆ ≤ ω − 1 + k holds, are considered. In particular, we find a set of graphs in which the minimal forbidden subgraphs for χ and ω coincide. Finally, we consider Υk in the universe of claw-free graphs and give a minimal subgraph characterization in terms of Turán graphs.
منابع مشابه
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