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Girth, oddness, and colouring defect of snarks
[article]
2022
arXiv
pre-print
The colouring defect of a cubic graph, introduced by Steffen in 2015, is the minimum number of edges that are left uncovered by any set of three perfect matchings. Since a cubic graph has defect 0 if and only if it is 3-edge-colourable, this invariant can measure how much a cubic graph differs from a 3-edge-colourable graph. Our aim is to examine the relationship of colouring defect to oddness, an extensively studied measure of uncolourability of cubic graphs, defined as the smallest number of
arXiv:2106.12205v3
fatcat:yod7bzzwafhp7gs4ykn34446xu