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Circular Coloring of Signed Bipartite Planar Graphs

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Extended Abstracts EuroComb 2021

Part of the book series: Trends in Mathematics ((RPCRMB,volume 14))

Abstract

In this work, we study the notion of circular coloring of signed graphs which is a refinement of 0-free 2k-coloring of signed graphs. The main question is that given a positive integer \(\ell \), what is the smallest even value \(f(\ell )\) such that for every signed bipartite (simple) planar graph \((G, \sigma )\) of negative-girth at least \(f(\ell )\), we have \(\chi _c(G, \sigma )\le \frac{2\ell }{\ell -1}\). We answer this question when \(\ell \) is small: \(f(2)=4, f(3)=6\) and \(f(4)=8\). The results fit into the framework of the bipartite analogue of the Jaeger-Zhang conjecture.

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Authors and Affiliations

  1. Université de Paris, CNRS, IRIF, 75013, Paris, France

    Reza Naserasr & Zhouningxin Wang

Authors
  1. Reza Naserasr
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  2. Zhouningxin Wang
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Corresponding author

Correspondence to Zhouningxin Wang .

Editor information

Editors and Affiliations

  1. Computer Science Institute, Charles University, Praha, Czech Republic

    Jaroslav Nešetřil

  2. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Guillem Perarnau

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Castelldefels, Spain

    Juanjo Rué

  4. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Oriol Serra

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Naserasr, R., Wang, Z. (2021). Circular Coloring of Signed Bipartite Planar Graphs. In: Nešetřil, J., Perarnau, G., Rué, J., Serra, O. (eds) Extended Abstracts EuroComb 2021. Trends in Mathematics(), vol 14. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-83823-2_33

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