Ramsey Numbers of Complete Bipartite Graphs

被引：0

作者：

Liu, Meng ^{[1
]}

Du, Bangwei ^{[1
]}

机构：

[1] Anhui Univ, Ctr Pure Math, Sch Math Sci, Hefei 230601, Anhui, Peoples R China

来源：

GRAPHS AND COMBINATORICS | 2025年 / 41卷 / 01期

关键词：

Ramsey number; Bipartite graph; Asymptotic bound;

D O I：

10.1007/s00373-025-02892-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let alpha>0 be a constant and let m >= 1 be an integer. In this short note, we shall show that R(K-m,K-alpha n,K-m,K-n)=((alpha(1/m)+1)(m)+o(1))n as n ->infinity

引用

页数：4

共 8 条

[1]

Burr S. A., 1973, UTILITAS MATHEMATICA, V4, P217

[2] MULTICOLOR RAMSEY NUMBERS FOR COMPLETE BIPARTITE GRAPHS [J].

CHUNG, FRK ;

GRAHAM, RL .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1975, 18 (02) :164-169

[3] Off-diagonal book Ramsey numbers [J].

Conlon, David ;

Fox, Jacob ;

Wigderson, Yuval .

COMBINATORICS PROBABILITY AND COMPUTING, 2023, 32 (03) :516-545

[4] A construction for Ramsey numbers for Km, n [J].

Dung, Lin ;

Li, Yusheng .

EUROPEAN JOURNAL OF COMBINATORICS, 2010, 31 (07) :1667-1670

[5]

FUREDI Z, 1996, COMB PROBAB COMPUT, V5, P29

[6]

Janson S., 2000, WIL INT S D, Vfirst

[7] Ramsey functions involving Km,n with n large [J].

Li, YS ;

Tang, XQ ;

Zang, WN .

DISCRETE MATHEMATICS, 2005, 300 (1-3) :120-128

[8] Off-diagonal and asymptotic results on the Ramsey number r(K2,m,K2,n) [J].

Lortz, R ;

Mengersen, I .

JOURNAL OF GRAPH THEORY, 2003, 43 (04) :252-268

← 1 →