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Volume 34 • Number 3 • 2011
 
• The Linear Arboricity of Planar Graphs with Maximum Degree at Least Five
Xiang Tan, Hongyu Chen and Jianliang Wu

Abstract.
Let G be a planar graph with maximum degree Δ5. It is proved that la(G)=Δ(G)/2 if (1) any 4-cycle is not adjacent to an i-cycle for any i{3,4,5} or (2) G has no intersecting 4-cycles and intersecting i-cycles for some i{3,6}.

2010 Mathematics Subject Classification: 05C15.


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