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 $\Delta\geq 5$. It is proved that $la(G)=\lceil\Delta(G)/2\rceil$ if (1) any 4-cycle is not adjacent to an $i$-cycle for any $i\in\{3,4,5\}$ or (2) $G$ has no intersecting 4-cycles and intersecting $i$-cycles for some $i\in \{3, 6\}$. 2010 Mathematics Subject Classification: 05C15. Full text: PDF