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On multiples of simple graphs and Vizing's Theorem
2010
Discrete Mathematics
Let G be a simple connected graph with maximum degree d, and let tG denote the graph obtained from G by replacing each edge with t parallel edges. Vizing's Theorem says that td ≤ χ (tG) ≤ td + t. When t = 1, i.e., when tG is a simple graph, Holyer proved that it is NP-hard to decide if χ (tG) = td + t or not. Here we show, using a recent result of Scheide, that when t > d/2 it is not NP-hard to answer this question, and in fact This characterization is best possible in the sense that for any
doi:10.1016/j.disc.2010.04.012
fatcat:gdpx4w2iqrg4vfuf6wghwzlod4