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- W2035278325 abstract "Wegner conjectured that the chromatic number of the square of any planar graph G with maximum degree Δ⩾8 is bounded by χ(G2)⩽⌊32Δ⌋+1. We prove the bound χ(G2)⩽⌈53Δ⌉+78. This is asymptotically an improvement on the previously best-known bound. For large values of Δ we give the bound of χ(G2)⩽⌈53Δ⌉+25. We generalize this result to L(p,q)-labeling of planar graphs, by showing that λqp(G)⩽q⌈53Δ⌉+18p+77q-18. For each of the results, the proof provides a quadratic time algorithm." @default.
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- W2035278325 date "2005-07-01" @default.
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- W2035278325 title "A bound on the chromatic number of the square of a planar graph" @default.
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- W2035278325 doi "https://doi.org/10.1016/j.jctb.2004.12.005" @default.
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