Vertex-arboricity of planar graphs without intersecting triangles

Authors:
Min Chen;André Raspaud;Weifan Wang
Affiliations:
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China and LaBRI UMR CNRS 5800, Universite Bordeaux I, 33405 Talence Cedex, France;LaBRI UMR CNRS 5800, Universite Bordeaux I, 33405 Talence Cedex, France;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Venue:
European Journal of Combinatorics
Year:
2012

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Abstract

The vertex-arboricity a(G) of a graph G is the minimum number of subsets into which vertex set V(G) can be partitioned so that each subset induces an acyclic graph. In this paper, we prove one of the conjectures proposed by Raspaud and Wang (2008) [15] which says that a(G)=2 for any planar graph without intersecting triangles.