Year: 2010
Type: preprint
Abstract: Let $c$ be an edge-colouring of a graph $G$ such that for every vertex $v$ there are at least $d \ge 2$ 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 $3 \times 2^{d-1}-2$.
Source: arXiv (Cornell University)
Author: Lo, Allan
Institution: University of Birmingham
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951484858