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On the linear vertex-arboricity of a planar graph. (English) Zbl 0705.05016
For a (simple) graph G, let the vertex linear arboricity \(\ell a(G)\) denote the minimum number of subsets into which the vertex set of G can be partitioned so that each subset induces a linear forest, that is, a forest whose components consist of simple paths. This note gives a nice proof of the following conjecture: If G is a (simple) planar graph, then \(\ell a(G)\leq 3\).
Reviewer: A.Tucker

MSC:
05C05 Trees
05C10 Planar graphs; geometric and topological aspects of graph theory
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