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The linear arboricity of planar graphs of maximum degree seven is four
Author(s) -
Wu JianLiang,
Wu YuWen
Publication year - 2008
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20305
Subject(s) - arboricity , combinatorics , mathematics , conjecture , planar graph , partition (number theory) , graph , degree (music) , simple graph , discrete mathematics , physics , acoustics
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