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arXiv · 2610.42019

Modulo k-orientations of highly edge-connected signed graphs

You Lu·Zhengke Miao·Zhenyu Tian·Cun-Quan Zhang
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Abstract

A modulo $k$-orientation of a signed graph is an orientation in which the outdegree and indegree are congruent modulo $k$ at every vertex. We show that, for every odd integer $k\ge3$, every essentially $k$-unbalanced $(6k-10)$-edge-connected signed graph admits a modulo $k$-orientation. This improves the edge-connectivity bound of Zhu [JCTB, 112 (2015)] from $6k-7$ to $6k-10$.

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You Lu, Zhengke Miao, Zhenyu Tian, Cun-Quan Zhang. 2026-10-30. Modulo k-orientations of highly edge-connected signed graphs. https://arxiv.org/abs/2610.42019

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