On the chromatic number of wheel-free graphs with no large bipartite graphs
نویسنده
چکیده
A wheel is an induced cycle C plus a vertex connected to at least three vertices of C. Trotignon [14] asked if the class of wheel-free graphs is χ-bounded, i.e. if the chromatic number of every graph with no induced copy of a wheel is bounded by a function of its maximal clique. In this paper, we prove a weaker statement: for every `, the class of graphs with no induced wheel and no induced K`,` is χ-bounded. Moreover, we show that the chromatic number of every triangle-free graph with no K`,` and no k-wheel (a cycle C plus a vertex incident to at least k vertices of C) is bounded. We also give some applications of these results on the chromatic number of graphs with no cycle with a fixed number of chords.
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تاریخ انتشار 2015