Brooks' theorem on powers of graphs
نویسندگان
چکیده
We prove that for k ≥ 3, the bound given by Brooks’ theorem on the chromatic number of k-th powers of graphs of maximum degree ∆ ≥ 3 can be lowered by 1, even in the case of online list coloring.
منابع مشابه
Duchet-type theorems for powers of HHD-free graphs
Using the idea due to P. DUCHET in proving his well–known theorem on powers of chordal graphs, we shall describe some theorems of DUCHET–type for powers of graphs that have no long induced cycles. In particular, our DUCHET–type theorem for HHD–free graphs improves a recent result due to DRAGAN, NICOLAI, BRANDSTÄDT saying that odd powers of HHD–free graphs are also HHD–free.
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عنوان ژورنال:
- Discrete Mathematics
دوره 325 شماره
صفحات -
تاریخ انتشار 2014