Covering Graphs by Cycles
β Scribed by Fan, Genghua
- Book ID
- 118198459
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 1992
- Tongue
- English
- Weight
- 687 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0895-4801
- DOI
- 10.1137/0405039
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract βIf G is a 2βconnected graph with n vertices and minimum degree d, then the vertices of G can be covered by less than n/d cycles. This settles a conjecture of Enomoto, Kaneko and Tuza for 2βconnected graphs.β
Some new results on minimum cycle covers are proved. As a consequence, it is obtained that the edges of a bridgeless graph G can be covered by cycles of total length at most |E(G)| + 25 24 (|V (G)| -1), and at most |E(G)| + |V (G)| -1 if G contains no circuit of length 8 or 12.
## Abstract Let __k__ and __n__ be two integers such that __k__ β₯ 0 and __n__ β₯ 3(__k__ + 1). Let __G__ be a graph of order __n__ with minimum degree at least β(__n__ + __k__)/2β. Then __G__ contains __k__ + 1 independent cycles covering all the vertices of __G__ such that __k__ of them are triangl