Abstract
The linear 2-arboricity of a graph G, denoted by la2(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. A 1-planar graph is a graph that can be drawn in the Euclidean plane such that each edge crosses at most one edge. An IC-planar is a 1-planar graph satisfying the condition that each vertex is incident with at most one crossing edge. It is shown in this paper that every IC-planar graph G with maximum degree Δ has la2(G)≤⌈Δ+12⌉+6.
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