Asymptotic bounds for some bipartite graph: Complete graph Ramsey numbers
type: Item
instance of: scholarly article
title: Asymptotic bounds for some bipartite graph: Complete graph Ramsey numbers
zbMATH Open document ID: 0953.05050
DOI: 10.1016/S0012-365X(99)00399-4
author: Yair Caro
author: Yusheng Li
author: Cecil Rousseau
author: Yuming Zhang
published in: Discrete Mathematics
publication date: 2001-01-29T00:00:00Z
review text: The authors define a variation on the usual Ramsey numbers: \(R_c(P^{\text{conv}}_e,t)\) is defined as the smallest integer \(n\) so that, if the vertices of the complete graph are cyclically ordered and its edges are \(t\)-colored, there exists a monochromatic path of length \(l\) which respects the order. \(R_c(C^{\text{conv}}_k, C_e^{\text{conv}})\) is similarly defined where \(C^{\text{conv}}_e\) refers to circuits for length \(l\) which respect the ordering. The authors prove several results including: Theorem 2.2. For positive integers \(l\) and \(t\), \(1+ l(l- 1)^{t-1}\leq R_c(P^{\text{conv}}_l,t)\leq 1+l^t\). Theorem 3.3. For positive integers \(l\) and \(k\), \[ (k-1)(l- 1)+ 1\leq R_c(C^{\text{conv}}_k, C^{\text{conv}}_l)\leq 2kl- 3k- 3l+ 6. \]
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 1462272
zbMATH Keywords: Ramsey numbers
zbMATH Keywords: complete graph
reviewed by: Jack E. Graver
MaRDI profile type: Publication
full work available at URL: s0012-365x(99)00399-4
OpenAlex ID: W2067803318
description: scientific article; zbMATH DE number 1462272