The linear 2-Arboricity of graph with mad(G) <10/3

Abstract

A linear 2-forest is a graph whose components are paths of length at most 2. The linear 2-Arboricity of a graph G, denoted by la₂(C), is the least number of linear 2-forests needed to decompose G. In this paper, we study the linear 2-Arboricity of a kind of sparse graph with mad{G) < 10/3 and prove that la₂(G) <+4 Δ(G)/2 +3 if 2 = 0,3 (mod 4); la₂{G) < Δ(G)/2+3 if Δ(G) Ξ 1,2 {mod 4). © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.