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

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 49, Issue 1, 2012, pp.145-154
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2012.49.1.145

Title & Authors

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

Chen, Hong-Yu; Tan, Xiang; Wu, Jian-Liang;

Chen, Hong-Yu; Tan, Xiang; Wu, Jian-Liang;

Abstract

Let G be a planar graph with maximum degree . The linear 2-arboricity (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) if G has no adjacent 3-cycles; (2) if G has no adjacent 4-cycles; (3) if any 3-cycle is not adjacent to a 4-cycle of G.

Keywords

planar graph;linear 2-arboricity;cycle;

Language

English

Cited by

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