Nowhere-zero 3-flows of graphs with prescribed sizes of odd edge cuts
β Scribed by Luo, Rong; Miao, Zhengke; Xu, Rui; Zhang, Cun-Quan
- Book ID
- 122859807
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 389 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0195-6698
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## Abstract A graph __G__ is an oddβcircuit tree if every block of __G__ is an odd length circuit. It is proved in this paper that the product of every pair of graphs __G__ and __H__ admits a nowhereβzero 3βflow unless __G__ is an oddβcircuit tree and __H__ has a bridge. This theorem is a partial r
Let G be a 2-edge-connected simple graph with order n. We show that if IV(G)l 5 17, then either G has a nowhere-zero 4-flow, or G is contractible to the Petersen graph. We also show that for n large, if Iβ¬(G)J L (' 2 17) + 34, then either G has a nonwhere-zero 4-flow, or G can be contracted to the P