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A note on shortest cycle covers of cubic graphs

✍ Scribed by Xinmin Hou; Cun-Quan Zhang

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 92 KB
Volume: 71
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20636

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✦ Synopsis

Abstract

Let SCC~3~(G) be the length of a shortest 3‐cycle cover of a bridgeless cubic graph G. It is proved in this note that if G contains no circuit of length 5 (an improvement of Jackson's (JCTB 1994) result: if G has girth at least 7) and if all 5‐circuits of G are disjoint (a new upper bound of SCC~3~(G) for the special class of graphs).

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