A Dirac type condition for properly coloured paths and cycles

Details A Dirac type condition for properly coloured paths and cycles A Dirac type condition for properly coloured paths and cycles

2010-08-19

arxiv.org/abs/1008.3242v2

Mathematics

Combinatorics

Scientific paper

Let $c$ be an edge colouring of a graph $G$ such that for every vertex $v$ there are at least $d$ different colours on edges incident to $v$. We prove that $G$ contains a properly coloured path of length 2d or a properly coloured cycle of length at least $d+1$. Moreover, if $G$ does not contain any properly coloured cycle, then there exists a properly coloured path of length $3 \times 2^{d-1}-2$.

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