Equitable Cluster Partition of Planar Graphs with Girth at Least 12  

作　　者：Xiaoling LIU Lei SUN Wei ZHENG 

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

出　　处：《Journal of Mathematical Research with Applications》2024年第2期152-160,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 equitable(O^(1)_(k),O^(2)_(k),...,O^(m)_(k))-partition of a graph G,which is also called a k cluster m-partition,is the partition of V(G)into m non-empty subsets V_(1),V_(2),...,Vm such that for every integer i in{1,2,...,m},G[Vi]is a graph with components of order at most k,and for each distinct pair i,j in{1,...,m},there is−1≤|Vi|−|Vj|≤1.In this paper,we proved that every planar graph G with minimum degreeδ(G)≥2 and girth g(G)≥12 admits an equitable(O_(1)^(7),O^(2)_(7),...,O^(m)_(7))-partition,for any integer m≥2.

关 键 词：equitable cluster partition planar graph GIRTH DISCHARGING 

分 类 号：O157.5[理学—数学]