Abstract
Abstract In 1977, Wegner conjectured that the chromatic number of the square of every planar graph G with maximum degree Δ ⩾ 8 is at most ⌈ 3 2 Δ ⌉ + 1 . We show that it is at most 3 2 Δ ( 1 + o ( 1 ) ) , and indeed this is true for the list chromatic number.
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