On strong edge-colouring of subcubic graphs

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...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2013-11, Vol.161 (16-17), p.2467-2479
Main Authors: Hocquard, Hervé, Montassier, Mickaël, Raspaud, André, Valicov, Petru
Format: Article
Language:English
Subjects:
Color
Colour
Computer Science
Discrete Mathematics
Graphs
Mathematical analysis
Maximum average degree
Optimization
Planar graphs
Strong edge-colouring
Subcubic graphs
Upper bounds
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Summary: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 73 (resp. 52, 83, 207) can be strongly edge-coloured with six (resp. seven, eight, nine) colours. These upper bounds are optimal except the one of 83. Also, we prove that every subcubic planar graph without 4-cycles and 5-cycles can be strongly edge-coloured with nine colours.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2013.05.021