On the linear 2-arboricity of planar graph without normally adjacent 3-cycles and 4-cycles

Abstract

ABSTRACTThe linear 2-arboricity of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests, whose components are paths of length at most 2. In this paper, we prove that if G is a planar graph in which there do not exist a 3-cycle and a 4-cycle sharing exactly one common edge, then . This improves some currently known results.