### Linear 2-arboricity of planar graphs without intersecting 5-cycles

CHEN Hong-yu, ZHONG Bin

1. School of Science, Shanghai Institute of Technology, Shanghai 201418, China
• Published:2020-07-08

Abstract: Let G be a planar graph without intersecting 5-cycles. If G is connected and δ(G)≥2, then G contains an edge xy with d(x)+d(y)≤10 or a 2-alternating cycle is proved. By this result, its linear 2-arboricity la2(G)≤「Δ/2+5 is obtained, which improves the known upper bound of la2(G) for planar graphs without 5-cycles.

Key words: planar graph, linear 2-arboricity, cycle

CLC Number:

• O5
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