The linear arboricity of planar graphs with no short cycles

Authors:
Jian-Liang Wu;Jian-Feng Hou;Gui-Zhen Liu
Affiliations:
School of Mathematics, Shandong University, Jinan, 250100, PR China;School of Mathematics, Shandong University, Jinan, 250100, PR China;School of Mathematics, Shandong University, Jinan, 250100, PR China
Venue:
Theoretical Computer Science
Year:
2007

Citing 3
Cited 3

Graph Theory With Applications

Graph Theory With Applications
On the linear arboricity of planar graphs

Journal of Graph Theory
The linear arboricity of planar graphs of maximum degree seven is four

Journal of Graph Theory

A planar linear arboricity conjecture

CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
A Planar LAC

Journal of Graph Theory
The linear arboricity of planar graphs with maximum degree at least 5

Information Processing Letters

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Abstract

The linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that @?@D(G)2@?@?la(G)@?@?@D(G)+12@? for any simple graph G. In the paper, it is proved that if G is a planar graph with @D=7 and without i-cycles for some i@?{4,5}, then la(G)=@?@D(G)2@?.