http://dx.doi.org/10.1016/j.disc.2012.03.035">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On the vertex-arboricity of planar graphs without 7-cycles

Language

English

Abstract

The vertex arboricity va(G) of a graph G is the minimum number of colors the vertices can be labeled so that each color class induces a forest. It was well-known that va(G)≤3 for every planar graph G. In this paper, we prove that va(G)≤2 if G is a planar graph without 7-cycles. This extends a result in [A. Raspaud, W. Wang, On the vertex-arboricity of planar graphs, European J. Combin. 29 (2008) 1064-1075] that for each k∈3,4,5,6, planar graphs G without k-cycles have va(G)≤2. © 2012 Elsevier B.V. All rights reserved.

Keywords

Cycle, Planar graph, Vertex arboricity

Publication Date

2012

Source Publication Title

Discrete Mathematics

Volume

312

Issue

15

Start Page

2304

End Page

2315

Publisher

Elsevier

ISSN (print)

0012365X

ISSN (electronic)

1872681X

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