Multicolored Bipartite Ramsey Numbers of Large Cycles  

作　　者：Shao-qiang LIU Yue-jian PENG 

机构地区：[1]College of Mathematics and Statistics,Hanshan Normal University,Chaozhou 521041,China [2]School of Mathematics,Hunan University,Changsha 410082,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第2期347-357,共11页应用数学学报（英文版）

基　　金：supported in part by National Natural Science Foundation of China(Grant No.11931002);the Department of Education of Guangdong Province Natural Science Foundation(Grant No.2020KTSCX078);the Project of Hanshan Normal University(Grant No.QN202024).

摘　　要：For an integer r≥2 and bipartite graphs Hi,where 1≤i≤r,the bipartite Ramsey number br(H1,H2,…,Hr)is the minimum integer N such that any r-edge coloring of the complete bipartite graph KN;N contains a monochromatic subgraph isomorphic to Hi in color i for some 1≤i≤r.We show that if r≥3;α1,α2>0,αj+2≥[(j+2)!-1]Σi=1^(j+1)α1 for j=1,2…r-2,then br(C2[α1n],C2[α2n],…,C2[αrn]=(Σ=j=1^(r)a j+o(1))n.

关 键 词：ramsey number bipartite ramsey number regularity lemma 

分 类 号：O157.5[理学—数学]