Brooks’ theorem on powers of graphs
Copyright policy )Brooks’ theorem on powers of graphs
We prove that for $k\geq 3$, the bound given by Brooks' theorem on the chromatic number of $k$-th powers of graphs of maximum degree $Δ\geq 3$ can be lowered by 1, even in the case of online list coloring.
7 pages, no figure, submitted
FOS: Computer and information sciences, Extremal problems in graph theory, Discrete Mathematics (cs.DM), [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Coloring of graphs and hypergraphs, Brooks' theorem, FOS: Mathematics, powers of graphs, Mathematics - Combinatorics, Combinatorics (math.CO), coloring, Computer Science - Discrete Mathematics
FOS: Computer and information sciences, Extremal problems in graph theory, Discrete Mathematics (cs.DM), [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Coloring of graphs and hypergraphs, Brooks' theorem, FOS: Mathematics, powers of graphs, Mathematics - Combinatorics, Combinatorics (math.CO), coloring, Computer Science - Discrete Mathematics
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