## Abstract Let __SCC__~3~(__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_
Shortest coverings of graphs with cycles
✍ Scribed by Jean Claude Bermond; Bill Jackson; François Jaeger
- Book ID
- 107884181
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 613 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0095-8956
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📜 SIMILAR VOLUMES
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.
## Abstract Let __k__ and __n__ be two integers such that __k__ ≥ 0 and __n__ ≥ 3(__k__ + 1). Let __G__ be a graph of order __n__ with minimum degree at least ⌈(__n__ + __k__)/2⌉. Then __G__ contains __k__ + 1 independent cycles covering all the vertices of __G__ such that __k__ of them are triangl