TY - JOUR

T1 - On the vertex-arboricity of planar graphs without 7-cycles

AU - Huang, Danjun

AU - SHIU, Wai Chee

AU - Wang, Weifan

N1 - Funding Information:
This work is supported partially by FRG, Hong Kong Baptist University, NSFC (No. 11071223 , No. 61170302 ), ZJNSF (No. Z6090150 ), ZSDZZZZXK08 and IP-OCNS-ZJNU.

PY - 2012/8/6

Y1 - 2012/8/6

N2 - 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.

AB - 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.

KW - Cycle

KW - Planar graph

KW - Vertex arboricity

UR - http://www.scopus.com/inward/record.url?scp=84861621263&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2012.03.035

DO - 10.1016/j.disc.2012.03.035

M3 - Article

AN - SCOPUS:84861621263

SN - 0012-365X

VL - 312

SP - 2304

EP - 2315

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 15

ER -