Discussiones Mathematicae Graph Theory 29(2) (2009)
275-292
doi: 10.7151/dmgt.1447
Jean-Luc Fouquet, Henri Thuillier, Jean-Marie Vanherpe
L.I.F.O., Faculté des Sciences, B.P. 6759 | Adam P. Wojda
Wydzia Matematyki Stosowanej |
In this paper we consider linear partitions of cubic simple graphs for which it is well known that la(G) = 2. A linear partition L = (L_{B},L_{R}) is said to be odd whenever each path of L_{B}∪L_{R} has odd length and semi-odd whenever each path of L_{B} (or each path of L_{R}) has odd length.
In [2] Aldred and Wormald showed that a cubic graph G is 3-edge colourable if and only if G has an odd linear partition. We give here more precise results and we study moreover relationships between semi-odd linear partitions and perfect matchings.
Keywords: Cubic graph, linear arboricity, strong matching, edge-colouring.
2000 Mathematics Subject Classification: Primary
05C70;
Secondary 05C38.
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Received 3 December 2007
Revised 13 June 2008
Accepted 13 June 2008