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

作　　者：Chunyu TIAN Lei SUN 

机构地区：[1]School of Mathematics and Statistics,Shandong Normal University,Shandong 250358,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第1期16-24,共9页数学研究及应用（英文版）

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).

摘　　要：An(O_(k1),O_(k2))-partition of a graph G is the partition of V(G)into two non-empty subsets V_(1) and V2,such that G[V_(1)]and G[V_(2)]are graphs with components of order at most k_(1) and k_(2),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(O_(2),O_(3))-partition,where i∈[6,7,8]and j∈[6,7,8,9].

关 键 词：planar graph FACE GIRTH vertex partition discharging procedure 

分 类 号：O157.5[理学—数学]