Long properly coloured cycles in edge-coloured graphs

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Colleges, School and Institutes


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 .

Bibliographic note

Lo A. Long properly coloured cycles in edge‐coloured graphs. J Graph Theory. 2019;90:416–442. https://doi.org/10.1002/jgt.22405


Original languageEnglish
Pages (from-to)416-442
Number of pages27
JournalJournal of Graph Theory
Issue number3
Early online date2 Nov 2018
Publication statusPublished - 1 Mar 2019