On linear arboricity of cubic graphs
نویسندگان
چکیده
A linear forest is a graph in which each connected component is a chordless path. 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. When each path has length at most k a linear forest is a linear k-forest and lak(G) will denote the minimum number of linear k-forests partitioning E(G). We clearly have lan−1(G) = la(G). In this paper we consider linear partitions of cubic simple graphs for which it is well known that la(G) = 2. We give a survey of already known results with new ones and new conjectures.
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