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Journal of Combinatorial Optimization

, Volume 35, Issue 2, pp 365–372 | Cite as

Vertex arboricity of planar graphs without intersecting 5-cycles

  • Hua Cai
  • Jianliang Wu
  • Lin Sun
Article

Abstract

The vertex arboricity va(G) of a graph G is the minimum number of colors the vertices can be colored so that each color class induces a forest. It was known that \(va(G)\le 3\) for every planar graph G. In this paper, we prove that \(va(G)\le 2\) if G is a planar graph without intersecting 5-cycles.

Keywords

Vertex arboricity Planar graph Cycle Intersecting Coloring 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsChangji UniversityChangjiPeople’s Republic of China
  2. 2.School of MathematicsShandong UniversityJinanPeople’s Republic of China

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