A Proof of a Conjecture on Bipartite Ramsey Numbers B(2,2,3)

Mathematics

Stanford Shateyi¹  Mostafa Gholami²  Yaser Rowshan² 

[1] Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa;Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 66731-45137, Iran;

关键词: Ramsey numbers;    bipartite Ramsey numbers;    Zarankiewicz number;   

DOI  :  10.3390/math10050701

来源: DOAJ

【 摘 要 】

The bipartite Ramsey number $B(n_1,n_2,\dots ,n_t)$ is the least positive integer b, such that any coloring of the edges of $K_{b,b}$ with t colors will result in a monochromatic copy of $K_{n_i,n_i}$ in the i-th color, for some i, $1\le i\le t$. The values $B(2,5)=17$, $B(2,2,2,2)=19$ and $B(2,2,2)=11$ have been computed in several previously published papers. In this paper, we obtain the exact values of the bipartite Ramsey number $B(2,2,3)$. In particular, we prove the conjecture on $B(2,2,3)$ which was proposed in 2015—in fact, we prove that $B(2,2,3)=17$.

【 授权许可】

Unknown