摘要
The linear 2-arboricity la2(G) of a graph 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 if G is a 1-planar graph with maximum degree Δ,then la_(2)(G)≤[(Δ+1)/2]+7.This improves a known result of Liu et al.(2019) that every 1-planar graph G has la_(2)(G)≤[(Δ+1)/2]+14.We also observe that there exists a 7-regular 1-planar graph G such that la2(G)=6=[(Δ+1)/2]+2,which implies that our solution is within 6 from optimal.
