A nowhere-zero 3-flow in a graph G is an assignment of a direction and a value of 1 or 2 to each edge of G such that, for each vertex v in G, the sum of the values of the edges with tail v equals the sum of the values of the edges with head v. Motivated by results about the region coloring of planar
Nowhere-zero flows in Cartesian bundles of graphs
✍ Scribed by Edita Rollová; Martin Škoviera
- Book ID
- 113582409
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 196 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0195-6698
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## Abstract In this paper, we characterize graphs whose tensor product admit nowhere‐zero 3‐flow. The main result is: For two graphs __G__~1~ and __G__~2~ with δ ≥ 2 and __G__~2~ not belonging to a well‐characterized class of graphs, the tensor product of __G__~1~ and __G__~2~ admits a nowhere‐zero
## Abstract A graph __G__ is an odd‐circuit 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 nowhere‐zero 3‐flow unless __G__ is an odd‐circuit tree and __H__ has a bridge. This theorem is a partial r
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