## Abstract It was conjectured by Fan that if a graph __G__ = (__V,E__) has a nowhereโzero 3โflow, then __G__ can be covered by two even subgraphs of total size at most |__V__| + |__E__| โ 3. This conjecture is proved in this paper. It is also proved in this paper that the optimum solution of the C
Integer flows
โ Scribed by D. H. Younger
- Publisher
- John Wiley and Sons
- Year
- 1983
- Tongue
- English
- Weight
- 404 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
A k-flow is an assignment of edge directions and integer weights in the range 1, ..., k -1 to the edges of an undirected graph so that at each vertex the flow in is equal to the flow out. This paper gives a polynomial algorithm for finding a 6-flow that applies uniformly to each graph. The algorithm specializes to give a 5-flow for planar graphs.
This paper was written while the author was a Visiting Scholar at Massachusetts Institute of Technology, on sabbatical leave from The University of Waterloo.
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