Nowhere-Zero 3-Flows of Graphs with Independence Number Two
β Scribed by Rong Luo, Zhengke Miao, Rui Xu
- Book ID
- 120788779
- Publisher
- Springer Japan
- Year
- 2012
- Tongue
- English
- Weight
- 224 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
## 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
## Abstract It is shown that the edges of a simple graph with a nowhereβzero 4βflow can be covered with cycles such that the sum of the lengths of the cycles is at most |__E__(__G__)| + |__V__(__G__)| β3. This solves a conjecture proposed by G. Fan.