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arXiv · 2204.05865

A note on shortest circuit cover of 3-edge colorable cubic signed graphs

Ronggui Xu·Jiaao Li·Xinmin Hou
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Abstract

A {sign-circuit cover} $\mathcal{F}$ of a signed graph $(G, σ)$ is a family of sign-circuits which covers all edges of $(G, σ)$. The shortest sign-circuit cover problem was initiated by Má$\check{\text{c}}$ajová, Raspaud, Rollová, and Škoviera (JGT 2016) and received many attentions in recent years. In this paper, we show that every flow-admissible 3-edge colorable cubic signed graph $(G, σ)$ has a sign-circuit cover with length at most $\frac{20}{9} |E(G)|$.

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Ronggui Xu, Jiaao Li, Xinmin Hou. 2022-04-12. A note on shortest circuit cover of 3-edge colorable cubic signed graphs. https://arxiv.org/abs/2204.05865

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