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 is said to be odd whenever each path of has odd length and semi-odd whenever each path of (or each path of ) 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1447,
author = {Jean-Luc Fouquet and Henri Thuillier and Jean-Marie Vanherpe and Adam P. Wojda},
title = {On odd and semi-odd linear partitions of cubic graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {29},
year = {2009},
pages = {275-292},
zbl = {1193.05130},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1447}
}
Jean-Luc Fouquet; Henri Thuillier; Jean-Marie Vanherpe; Adam P. Wojda. On odd and semi-odd linear partitions of cubic graphs. Discussiones Mathematicae Graph Theory, Tome 29 (2009) pp. 275-292. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1447/
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