English

Strong edge-colouring of sparse planar graphs

Discrete Mathematics 2014-07-22 v3 Combinatorics

Abstract

A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching. It is known that every planar graph with maximum degree Δ\Delta has a strong edge-colouring with at most 4Δ+44\Delta+4 colours. We show that 3Δ+13\Delta+1 colours suffice if the graph has girth 6, and 4Δ4\Delta colours suffice if Δ7\Delta\geq 7 or the girth is at least 5. In the last part of the paper, we raise some questions related to a long-standing conjecture of Vizing on proper edge-colouring of planar graphs.

Keywords

Cite

@article{arxiv.1401.4568,
  title  = {Strong edge-colouring of sparse planar graphs},
  author = {Julien Bensmail and Ararat Harutyunyan and Hervé Hocquard and Petru Valicov},
  journal= {arXiv preprint arXiv:1401.4568},
  year   = {2014}
}
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