The linear 2-arboricity of 1-planar graphs without 3-cycles

Abstract

The linear 2-arboricity la[Formula: see text] of a graph [Formula: see text] is the least integer [Formula: see text] such that [Formula: see text] can be partitioned into [Formula: see text] edge-disjoint forests, whose component trees are paths of length at most 2. In this paper, we prove that if [Formula: see text] is a 1-planar graph without 3-cycles and with maximum degree [Formula: see text], then la[Formula: see text].