Star-factorization of the Complete Bipartite Multigraphs  

作　　者：Jing SHI Jian WANG Bei-liang DU 

机构地区：[1]School of Science,Nantong University,Nantong 226007,China [2]Department of Mathematics,Suzhou University,Suzhou 215006,China [3]Mathematics Teaching and Research Office,Nantong Vocational College,Nantong 226007,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第2期239-248,共10页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No.K110703711)。

摘　　要：LetλK_(m,n)be a complete bipartite multigraph with two partite sets having m and n vertices,respectively.A K_(p,q)-factorization ofλK_(m,n)is a set of K_(p,q)-factors ofλK_(m,n)which partition the set of edges ofλK_(m,n).Whenλ=1,Martin,in[Complete bipartite factorizations by complete bipartite graphs,Discrete Math.,167/168(1997),461–480],gave simple necessary conditions for such a factorization to exist,and conjectured those conditions are always sufficient.In this paper,we will study the K_(p,q)-factorization ofλK_(m,n)for p=1,to show that the necessary conditions for such a factorization are always sufficient whenever related parameters are sufficiently large.

关 键 词：complete bipartite multigraph STAR FACTORIZATION 

分 类 号：O157.5[理学—数学]