THE LINEAR 2-ARBORICITY OF PLANAR GRAPHS WITHOUT ADJACENT SHORT CYCLES

Title & Authors
THE LINEAR 2-ARBORICITY OF PLANAR GRAPHS WITHOUT ADJACENT SHORT CYCLES
Chen, Hong-Yu; Tan, Xiang; Wu, Jian-Liang;

Abstract
Let G be a planar graph with maximum degree $\small{\Delta}$. The linear 2-arboricity $\small{la_2}$(G) of G is the least integer k such that G can be partitioned into k edge-disjoint forests, whose component trees are paths of length at most 2. In this paper, we prove that (1) $\small{la_2(G){\leq}{\lceil}\frac{\Delta}{2}\rceil+8}$ if G has no adjacent 3-cycles; (2) $\small{la_2(G){\leq}{\lceil}\frac{\Delta}{2}\rceil+10}$ if G has no adjacent 4-cycles; (3) $\small{la_2(G){\leq}{\lceil}\frac{\Delta}{2}\rceil+6}$ if any 3-cycle is not adjacent to a 4-cycle of G.
Keywords
planar graph;linear 2-arboricity;cycle;
Language
English
Cited by
1.
On the linear 2-arboricity of planar graph without normally adjacent 3-cycles and 4-cycles, International Journal of Computer Mathematics, 2017, 94, 5, 981
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