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On strong edge-colouring of subcubic graphs

Abstract : A strong edge-colouring of a graph G is a proper edge-colouring such that every path of length 3 uses three different colours. In this paper we improve some previous results on the strong edge-colouring of subcubic graphs by showing that every subcubic graph with maximum average degree strictly less than 7/3 (resp. 5/2, 8/3, 20/7) can be strongly edge-coloured with six (resp. seven, eight, nine) colours. These upper bounds are optimal except the one of 8/3. Also, we prove that every subcubic planar graph without 4-cycles and 5-cycles can be strongly edge-coloured with nine colours.
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https://hal.archives-ouvertes.fr/hal-00686021
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Submitted on : Wednesday, January 23, 2013 - 10:26:19 AM
Last modification on : Monday, August 31, 2020 - 9:52:21 AM
Long-term archiving on: : Wednesday, April 24, 2013 - 3:54:51 AM

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Hervé Hocquard, Mickael Montassier, André Raspaud, Petru Valicov. On strong edge-colouring of subcubic graphs. Discrete Applied Mathematics, Elsevier, 2013, 161 (16-17), pp.2467-2479. ⟨10.1016/j.dam.2013.05.021⟩. ⟨hal-00686021v2⟩

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