CDAM Research Report, LSE-CDAM-2008-09
List Coloring Squares of Planar Graphs
Frédéric Havet, Jan van den Heuvel, Colin McDiarmid and Bruce ReedIn 1977, Wegner conjectured that the chromatic number of the square of every planar graph G with maximum degree Δ ≥ 8 is at most ⌊3Δ⁄2⌋ + 1. We show that it is at most 3Δ⁄2(1+o(1)), and indeed this is true for the list chromatic number and for more general classes of graphs.
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