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On odd and semi-odd linear partitions of cubic graphs

Jean-Luc FouquetHenri ThuillierJean-Marie VanherpeAdam P. Wojda — 2009

Discussiones Mathematicae Graph Theory

A linear forest is a graph whose connected components are chordless paths. A linear partition of a graph G is a partition of its edge set into linear forests and la(G) is the minimum number of linear forests in a linear partition. 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...

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