We show that the edge set of a bridgeless cubic graph \(G\) can be covered with circuits such that the sum of the lengths of the circuits is at most \(\frac{64}{39}|E(G)|\). Stronger results are obtained for cubic graphs of large girth. 1994 Academic Press, Inc.
โฆ LIBER โฆ
Small Circuit Double Covers of Cubic Multigraphs
โ Scribed by H.J. Lai; X.X. Yu; C.Q. Zhang
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 499 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
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## 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 __