A note on shortest cycle covers of cubic graphs

Let SCC3(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 SCC3(G) for the special class of graphs). © 2012 Wiley Periodicals, Inc.

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