## Abstract Let __SCC__~3~(__G__) be the length of a shortest 3βcycle 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 5βcircuits of __G_
Shortest Circuit Covers of Cubic Graphs
β Scribed by B. Jackson
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 298 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0095-8956
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β¦ Synopsis
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.
π SIMILAR VOLUMES
## Abstract Let __G__ be a bridgeless cubic graph. We prove that the edges of __G__ can be covered by circuits whose total length is at most (44/27) |__E(G)__|, and if Tutte's 3βflow Conjecture is true, at most (92/57) |__E(G)__|.
## Abstract In this paper, we focus our attention on joinβcovered graphs, that is, Β±1βweighted graphs, without negative circuits, in which every edge lies in a zeroβweight circuit. Join covered graphs are a natural generalization of matchingβcovered graphs. Many important properties of matching cov
An equivalent statement of the circuit double cover conjecture is that every bridgeless graph \(G\) has a circuit cover such that each vertex \(v\) of \(G\) is contained in at most \(d(v)\) circuits of the cover, where \(d(v)\) is the degree of \(v\). Pyber conjectured that every bridgeless graph \(