Circuit extension and circuit double cover of graphs
β Scribed by Miao, Zhengke; Ye, Dong; Zhang, Cun-Quan
- Book ID
- 120544186
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 393 KB
- Volume
- 313
- Category
- Article
- ISSN
- 0012-365X
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## 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
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.
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 \(