5-colouring graphs with 4 crossings
Abstract
We disprove a conjecture of Oporowski and Zhao stating that every graph with crossing number at most 5 and clique number at most 5 is 5-colourable. However, we show that every graph with crossing number at most 4 and clique number at most 5 is 5-colourable. We also show some colourability results on graphs that can be made planar by removing few edges. In particular, we show that if there exists three edges whose removal leaves the graph planar then it is 5-colourable.
Domains
Discrete Mathematics [cs.DM]
Origin : Files produced by the author(s)
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