5-colouring graphs with 4 crossings
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چکیده
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 a graph with clique number at most 5 has three edges whose removal leaves the graph planar, then it is 5-colourable.
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تاریخ انتشار 2009