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Modulo k-orientations of highly edge-connected signed graphs
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≥3, 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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BibTeX
@misc{lu2026modulo,
title = {{Modulo k-orientations of highly edge-connected signed graphs}},
author = {You Lu and Zhengke Miao and Zhenyu Tian and Cun-Quan Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42019},
eprint = {2610.42019},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42019},
}
RIS
TY - UNPB
TI - Modulo k-orientations of highly edge-connected signed graphs
AU - You Lu
AU - Zhengke Miao
AU - Zhenyu Tian
AU - Cun-Quan Zhang
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42019
UR - https://arxiv.org/abs/2610.42019
AB - 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≥3, 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.
ER -