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A note on shortest cycle covers of cubic graphs |
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| Authors: | Xinmin Hou Cun‐Quan Zhang |
| Institution: | 1. Department of Mathematics, University of Science and Technology of China, , Hefei, Anhui, 230026 P. R. China;2. Department of Mathematics, West Virginia University, , Morgantown, West Virginia, 26506‐6310 |
| Abstract: | 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). |
| Keywords: | cycle cover perfect matching 2‐factor shortest cycle cover |