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

The linear 2-arboricity la 2 (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 without 3-cycles and with maximum degree Δ , then la 2 (G) ≤ ⌈ Δ + 1 2 ⌉ + 6. [ABSTRACT FROM AUTHOR]