In this paper, we obtained some necessary and sufficient conditions for a graph having 5, 6and 7-cycle double covers, etc. We also provide a few necessary and sufficient conditions for a graph admitting a nowhere-zero 4-flow. With the aid of those basic properties of nowhere-zero 4flow and the resul
Flows, flow-pair covers and cycle double covers
β Scribed by Dezheng Xie; Cun-Quan Zhang
- Book ID
- 108114053
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 433 KB
- Volume
- 309
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
## Abstract It was conjectured by Fan that if a graph __G__ = (__V,E__) has a nowhereβzero 3βflow, then __G__ can be covered by two even subgraphs of total size at most |__V__| + |__E__| β 3. This conjecture is proved in this paper. It is also proved in this paper that the optimum solution of the C