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The linear arboricity of planar graphs of maximum degree seven is four

✍ Scribed by Jian-Liang Wu; Yu-Wen Wu

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 130 KB
Volume: 58
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20305

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✦ Synopsis

Abstract

The linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama et al. conjectured that $\lceil {\Delta {({G})}\over {2}}\rceil \leq {la}({G}) \leq \lceil {\Delta({G})+{1}\over {2}}\rceil$ for any simple graph G. Wu wu proved the conjecture for a planar graph G of maximum degree $\Delta\not={{7}}$. It is noted here that the conjecture is also true for $\Delta={{7}}$. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:210‐220, 2008

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