Tree-chromatic number
نویسنده
چکیده
Let us say a graph G has “tree-chromatic number” at most k if it admits a tree-decomposition (T, (Xt : t ∈ V (T ))) such that G[Xt] has chromatic number at most k for each t ∈ V (T ). This seems to be a new concept, and this paper is a collection of observations on the topic. In particular we show that there are graphs with tree-chromatic number two and with arbitrarily large chromatic number; and for all l ≥ 4, every graph with no triangle and with no induced cycle of length more than l has tree-chromatic number at most l− 2.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 116 شماره
صفحات -
تاریخ انتشار 2016