On Some Cycles in Wenger Graphs

作     者：Ye WANG Felix LAZEBNIK Andrew THOMASON Ye WANG;Felix LAZEBNIK;Andrew THOMASON

作者机构：College of Mathematical SciencesHarbin Engineering UniversityHarbin 150001China Department of Mathematical SciencesUniversity of DelawareNewark.DE 19716U.S.A. DPMMSCentre for Mathematical SciencesWilberforce RoadCambridgeUK 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2020年第36卷第2期

页      面：492-502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 NSF grant DMS-1106938-002,NSFC(Nos.11701372.11801371) Shanghai Sailing Program(No.19YF1435500) 

主　　题：cycle pancyclic finite field Wenger graph graph embeddings 

摘      要：Let p be a prime,q be a power of p,and let Fq be the field of q *** any positive integer n,the Wenger graph Wn(q)is defined as follows:it is a bipartite graph with the vertex partitions being two copies of the(n+1)-dimensional vector space Fq^n+1,and two vertices p=(p(1),…,p(n+1))and l=[l(1),…,l(n+1)]being adjacent if p(i)+l(i)=p(1)l(1)i-1,for all i=2,3,…,n+*** 2008,Shao,He and Shan showed that for n≥2,Wn(q)contains a cycle of length 2 k where 4≤k≤2 p and k≠*** this paper we extend their results by showing that(i)for n≥2 and p≥3,Wn(q)contains cycles of length 2k,where 4≤k≤4 p+1 and k≠5;(ii)for q≥5,0c1,and every integer k,3≤k≤qc,if 1≤n(1-c-7/3 logq2)k-1,then Wn(q)contains a 2 *** particular,Wn(q)contains cycles of length 2 k,where n+2≤k≤qc,provided q is sufficiently large.