Long properly coloured cycles in edge-coloured graphs |
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Authors: | Allan Lo |
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Institution: | School of Mathematics, University of Birmingham, Birmingham, UK |
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Abstract: | Let be an edge-coloured graph. The minimum colour degree of is the largest integer such that, for every vertex , there are at least distinct colours on edges incident to . We say that is properly coloured if no two adjacent edges have the same colour. In this paper, we show that, for any and large, every edge-coloured graph with contains a properly coloured cycle of length at least . |
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Keywords: | colour degree cycle proper edge-colouring |
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