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A Note on Shortest Sign-Circuit Cover of Signed 3-Edge-Colorable Cubic Graphs

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Abstract

A sign-circuit cover \({\mathcal {F}}\) of a signed graph \((G, \sigma )\) is a family of sign-circuits which covers all edges of \((G, \sigma )\). 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 signed 3-edge-colorable cubic graph \((G, \sigma )\) has a sign-circuit cover with length at most \(\frac{20}{9} |E(G)|\).

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Authors and Affiliations

  1. School of Data Science, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Ronggui Xu & Xinmin Hou

  2. School of Mathematical Sciences, Nankai University, Tianjin, 300071, China

    Jiaao Li

  3. CAS Key Laboratory of Wu Wen-Tsun Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Xinmin Hou

  4. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Xinmin Hou

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  1. Ronggui Xu
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Correspondence to Xinmin Hou.

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No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.

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The work was supported by National Natural Science Foundation of China (No. 12071453) and the National Key R and D Program of China(2020YFA0713100) and Anhui Initiative in Quantum Information Technologies (AHY150200) and the Innovation Program for Quantum Science and Technology, China (2021ZD0302904).

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Xu, R., Li, J. & Hou, X. A Note on Shortest Sign-Circuit Cover of Signed 3-Edge-Colorable Cubic Graphs. Graphs and Combinatorics 38, 144 (2022). https://doi.org/10.1007/s00373-022-02554-3

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  • DOI: https://doi.org/10.1007/s00373-022-02554-3

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