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Title of Journal: Graphs and Combinatorics

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Abbravation: Graphs and Combinatorics

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Springer Japan

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DOI

10.1002/malq.19800262502

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1435-5914

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Cubic Bridgeless Graphs and Braces

Authors: Andrea Jiménez Mihyun Kang Martin Loebl
Publish Date: 2016/07/01
Volume: 32, Issue: 6, Pages: 2473-2495
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Abstract

There are many longstanding 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 graphsAndrea Jiménez partially supported by CONICYT FONDECYT/POSTDOCTORADO 3150673 Núcleo Milenio Información y Coordinación en Redes ICM/FIC RC130003 Chile FAPESP Proc 2013/034476 and CNPq Proc 456792/20147 Brazil Mihyun Kang partially supported by the German Research Foundation KA 2748/21 and KA 2748/31 Martin Loebl partially supported by the Czech Science Foundation under the Contract Number P2021321988S

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  2. Exponentially Many Monochromatic n -Matchings in K 3 n -1
  3. The Linear Arboricity of Planar Graphs without 5-, 6-Cycles with Chords
  4. $$[1,1,t]$$-Colorings of Complete Graphs
  5. A Criterion for a Pair of Convex Polygons to be Reversible
  6. Bipartite Divisor Graphs for Integer Subsets
  7. The Ramsey property for collections of sequences not containing all arithmetic progressions
  8. Minimum Clique Partition in Unit Disk Graphs
  9. Graphs with a Minimal Number of Convex Sets
  10. Monochromatic Solutions for Multi-Term Unknowns
  11. Collapsible Graphs and Hamiltonicity of Line Graphs
  12. Collapsible Graphs and Hamiltonicity of Line Graphs
  13. Local Antimagic Vertex Coloring of a Graph
  14. Graph Equation for Line Graphs and m -Step Graphs
  15. A Description of the Resonance Variety of a Line Combinatorics via Combinatorial Pencils
  16. Monitoring the Plane with Rotating Radars
  17. Perfect Matchings in Total Domination Critical Graphs
  18. The Interchange Graphs of Tournaments with Minimum Score Vectors Are Exactly Hypercubes
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