Cycle covers of cubic multigraphs
β Scribed by Brian Alspach; Cun-Quan Zhang
- Book ID
- 103056297
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 446 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Alspach, B. and C.-Q. Zhang, Cycle covers of cubic multigraphs, Discrete Mathematics 111 (1993) 11-17.
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 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_
## Abstract In this paper we establish necessary and sufficient conditions for decomposing the complete multigraph Ξ»__K__~__n__~ into cycles of length Ξ», and the Ξ»βfold complete symmetric digraph Ξ»__K__ into directed cycles of length Ξ». As a corollary to these results we obtain necessary and suffic
It is shown that the obvious necessary conditions for the existence of a decomposition of the complete multigraph with n vertices and with k edges joining each pair of distinct vertices into m-cycles, or into m-cycles and a perfect matching, are also sufficient. This result follows as an easy conseq