Poh, K. S. On the linear vertex-arboricity of a planar graph. (English) Zbl 0705.05016 J. Graph Theory 14, No. 1, 73-75 (1990). 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 Cited in 2 ReviewsCited in 45 Documents MSC: 05C05 Trees 05C10 Planar graphs; geometric and topological aspects of graph theory Keywords:vertex linear arboricity PDFBibTeX XMLCite \textit{K. S. Poh}, J. Graph Theory 14, No. 1, 73--75 (1990; Zbl 0705.05016) Full Text: DOI References: [1] Akiyama, Path chromatic numbers of graphs · Zbl 0688.05024 [2] and , Generalized colorings of outerplanar and planar graphs. Proceedings, Fifth International Conference on the Theory and Applications of Graphs with Special Emphasis on Algorithms and Computer Science Applications, Wiley–Interscience, New York (1984) 151–161. [3] Chartrand, Proc. Camb. Phil. Soc. 64 pp 265– (1968) [4] Chartrand, J. Lond. Math. Soc. 44 pp 612– (1969) [5] Chartrand, Israel J. Math. 6 pp 169– (1968) [6] Cowen, J. Graph Theory 10 pp 187– (1986) [7] Conditional colorability in graphs. Proceedings, First Colorado Symposium on Graph Theory, Wiley–Interscience, New York (1984) 127–136. [8] Bounds for the vertex linear arboricity, to appear. · Zbl 0705.05018 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.