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Strong edge-colouring and induced matchings

Hervé Hocquard 1 Pascal Ochem 2 Petru Valicov 3, *
* Corresponding author
2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A strong edge-colouring of a graph G is a proper edge-colouring such that every path of three edges uses three distinct colours. An induced matching of a graph G is a subset I of edges of G such that the graph induced by the endpoints of I is a matching. In this paper, we prove the NP-completeness of strong 4, 5 and 6-edge-colouring and maximum induced matching in the case of some restricted subclasses of subcubic planar graphs. We also obtain a tight upper bound for the minimum number of colours in a strong edge-colouring of outerplanar graphs as a function of the maximum degree.
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Submitted on : Sunday, July 28, 2013 - 3:03:42 PM
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Hervé Hocquard, Pascal Ochem, Petru Valicov. Strong edge-colouring and induced matchings. Information Processing Letters, Elsevier, 2013, 113 (19-21), pp.836-843. ⟨10.1016/j.ipl.2013.07.026⟩. ⟨hal-00609454v4⟩

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