Modulo orientations with bounded out-degrees

Morteza Hasanvand

paper

Modulo orientations with bounded out-degrees

arXiv:1702.07039

Abstract

Let $G$ be a graph, let $k$ be a positive integer, and let $p : V (G) \to Z_{k}$ be a mapping with $∣ E (G) ∣ \equiv k \sum_{v \in V (G)} p (v)$ . In this paper, we show that if $G$ is $(3 k - 3)$ -edge-connected, then it has an orientation such that for each vertex $v$ , $∣ d_{G}^{+} (v) - d_{G} (v) /2∣ < k$ ; also if $G$ contains $2 k - 2$ edge-disjoint spanning trees, then it admits such an orientation but by imposing greater out-degree bounds.

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