《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (7): 38-45.

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### 不含相交5-圈的平面图的线性2-荫度

1. 上海应用技术大学理学院, 上海 201418
• 发布日期:2020-07-08
• 作者简介:陈宏宇(1981— ),女,博士,副教授,研究方向为图论. E-mail:hongyuchen86@163.com
• 基金资助:
国家自然科学基金青年科学基金资助项目(11401386);上海应用技术大学中青年科技人才发展基金

### 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

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