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Graphs and Combinatorics

, Volume 32, Issue 6, pp 2473–2495 | Cite as

Cubic Bridgeless Graphs and Braces

  • Andrea Jiménez
  • Mihyun Kang
  • Martin Loebl
Original Paper
  • 122 Downloads

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.

Keywords

Cubic graphs Braces Perfect matchings Directed cycles double cover 

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Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.CIMFAV, Facultad de IngenieríaUniversidad de ValparaísoValparaisoChile
  2. 2.Institute of Discrete MathematicsGraz University of TechnologyGrazAustria
  3. 3.Department of Applied MathematicsCharles UniversityPragueCzech Republic

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