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Cubic Bridgeless Graphs and Braces

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Abstract

There are many long-standing open problems on cubic bridgeless graphs, for instance, Jaeger’s directed cycle double cover conjecture. On the other hand, many structural properties of braces have been recently discovered. In this work, we bijectively map the cubic bridgeless graphs to braces which we call the hexagon graphs, and explore the structure of hexagon graphs. We show that hexagon graphs are braces that can be generated from the ladder on 8 vertices using two types of McCuaig’s augmentations. In addition, we present a reformulation of Jaeger’s directed cycle double cover conjecture in the class of hexagon graphs.

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Authors and Affiliations

  1. CIMFAV, Facultad de Ingeniería, Universidad de Valparaíso, Valparaiso, Chile

    Andrea Jiménez

  2. Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria

    Mihyun Kang

  3. Department of Applied Mathematics, Charles University, Prague, Czech Republic

    Martin Loebl

Authors
  1. Andrea Jiménez
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  2. Mihyun Kang
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  3. Martin Loebl
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Corresponding author

Correspondence to Andrea Jiménez.

Additional information

Andrea Jiménez partially supported by CONICYT: FONDECYT/POSTDOCTORADO 3150673, Núcleo Milenio Información y Coordinación en Redes ICM/FIC RC130003, Chile, FAPESP (Proc. 2013/03447-6) and CNPq (Proc. 456792/2014-7), Brazil. Mihyun Kang partially supported by the German Research Foundation KA 2748/2-1 and KA 2748/3-1). Martin Loebl partially supported by the Czech Science Foundation under the Contract Number P202-13-21988S.

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Jiménez, A., Kang, M. & Loebl, M. Cubic Bridgeless Graphs and Braces. Graphs and Combinatorics 32, 2473–2495 (2016). https://doi.org/10.1007/s00373-016-1722-y

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  • DOI: https://doi.org/10.1007/s00373-016-1722-y

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