A Note on 5-Cycle Double Covers
β Scribed by Arthur Hoffmann-Ostenhof
- Book ID
- 120788713
- Publisher
- Springer Japan
- Year
- 2012
- Tongue
- English
- Weight
- 99 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
It is shown that if a graph has a cycle double cover, then its line graph also has a cycle double cover. The converse of this result for 2-edge-connected graphs would imply the truth of the cycle double cover conjecture. Cycle Double Cover Conjecture (CDCC). Every 2-edge-connected graph has a CDC.
## 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_
Let O(G) denote the set of odd-degree vertices of a graph G. Let t E N and let 9, denote the family of graphs G whose edge set has a partition This partition is associated with a double cycle cover of G. We show that if a graph G is at most 5 edges short of being 4-edge-connected, then exactly one