Generalised acyclic edge colourings of graphs with large girth
Generalised acyclic edge colourings of graphs with large girth
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DOI：
10.1016/j.disc.2006.09.004
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发表时间：
2007-06
期刊：
影响因子：
--
通讯作者：
S. Gerke;Melanie Raemy
中科院分区：
文献类型：
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作者：
S. Gerke;Melanie Raemy
图G的r-无圈边色数是为图G的边着色所需的最小色数，使得相邻的边得到不同的颜色，并且每个圈C至少得到min{|C|，r}个颜色。证明了对任意整数r⩾4，围长至少为3(r-1)Δ且最大度为Δ的图G的r-无圈边色数至多为6(r-1)Δ.
The r-acyclic edge chromatic number of a graph G is the minimum number of colours required to colour the edges of G in such a way that adjacent edges receive different colours and every cycle C receives at least min{|C|,r} colours. We prove that for any integer r⩾4, the r-acyclic edge chromatic number of any graph G with maximum degree Δ and with girth at least 3(r-1)Δ is at most 6(r-1)Δ.