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Small cycle double covers of products I: Lexicographic product with paths and cycles
Article first published online: 15 NOV 2007
DOI: 10.1002/jgt.20265
Copyright © 2007 Wiley Periodicals, Inc.
1097-0118/asset/cover.gif?v=1&s=747ee645df081de59c78864878c8bdb9daeca9a1 "Journal of Graph Theory")
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How to Cite
Nowakowski, R. J. and Seyffarth, K. (2008), Small cycle double covers of products I: Lexicographic product with paths and cycles. Journal of Graph Theory, 57: 99–123. doi: 10.1002/jgt.20265
Publication History
- Issue published online: 11 DEC 2007
- Article first published online: 15 NOV 2007
- Manuscript Revised: 10 JUL 2007
- Manuscript Received: 21 JUN 2001
Funded by
- Natural Sciences and Engineering Research Council (to R.J.N. and K.S.)
- Abstract
- References
- Cited By
Keywords:
- cycle double cover;
- lexicographic product;
- matchings
Abstract
Bondy conjectured that every simple bridgeless graph has a small cycle double cover (SCDC). We show that this is the case for the lexicographic products of certain graphs and along the way for the Cartesian product as well. Specifically, if G does not have an isolated vertex then G □ P2 and G □ C2k have SCDCs. If G has an SCDC then so does G □ Pk, k > 2 and G □ C2k + 1. We use these Cartesian results to show that P2j[G] (j ≥ 1) and Ck[G] (k ≠ 3, 5, 7) have SCDCs. Also, if G has an SCDC then so does P2j + 1[G] (j ≥ 4). The results for the lexicographic product are harder and, in addition to the Cartesian results, require certain decompositions of Kn,n into perfect matchings. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 99–123, 2008