Partitioning Planar Graphs with Girth at Least 6 into Bounded Size Components

作     者：Chunyu TIAN Lei SUN Chunyu TIAN;Lei SUN

作者机构：School of Mathematics and Statistics Shandong Normal University 

出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文版))

年 卷 期：2023年第43卷第1期

页      面：16-24页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos. 12071265 12271331) the Natural Science Foundation of Shandong Province (Grant No. ZR202102250232) 

主　　题：planar graph face girth vertex partition discharging procedure 

摘      要：An(Ok1、Ok2)-partition of a graph G is the partition of V(G) into two non-empty subsets V1and V2,such that G[V1] and G[V2] are graphs with components of order at most k1and k2,respectively.In this paper,we consider the problem of partitioning the vertex set of a planar graph with girth restriction such that each part induces a graph with components of bounded order.We prove that every planar graph with girth at least 6 and i-cycle is not intersecting with j-cycle admits an(O2,O3)-partition,where i∈{6,7,8} and j∈{6,7,8,9}.