Discussiones Mathematicae Graph Theory 30(2) (2010) 315-333
doi: 10.7151/dmgt.1496

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Mácajová and Skoviera Conjecture on Cubic Graphs

Jean-Luc Fouquet  and  Jean-Marie Vanherpe

L.I.F.O., Faculté des Sciences, B.P. 6759
Université d'Orléans, 45067 Orléans Cedex 2, France


A conjecture of Mácajová and Skoviera asserts that every bridgeless cubic graph has two perfect matchings whose intersection does not contain any odd edge cut. We prove this conjecture for graphs with few vertices and we give a stronger result for traceable graphs.

Keywords: Cubic graph, edge-partition, traceable graphs.

2010 Mathematics Subject Classification: 05C30, 05C70.


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Received 31 December 2008
Revised 12 September 2009
Accepted 9 November 2009