A note on zero-sum 5-flows in regular graphs

Details A note on zero-sum 5-flows in regular graphs A note on zero-sum 5-flows in regular graphs

2011-08-15

arxiv.org/abs/1108.2950v1

Mathematics

Combinatorics

Scientific paper

Let $G$ be a graph. A zero-sum flow in $G$ is an assignment of nonzero real number to the edges such that the sum of the values of all edges incident with each vertex is zero. Let $k$ be naturel number. A zero-sum $k$-flow is a flow with value from the set $\{\pm 1, \pm 2,..., \pm(k-1)\}$. It has been conjectured that every $r$-regular graph, $r\geq 3$, admits a zero-sum 5-flow. In this paper we give an affirmative answer to this conjecture, exept for r=5.

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