On \((t-1)\)-colored paths in \(t\)-colored complete graphs
type: Item
instance of: scholarly article
title: On \((t-1)\)-colored paths in \(t\)-colored complete graphs
zbMATH Open document ID: 1414.05190
author: Amir Khamseh
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2018-08-10T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1530065009
review text: Given $t$ distinct colors, the $t$ subsets of $t-1$ colors are ordered in some arbitrary manner. Let $(G_1, G_2, \ldots, G_t)$ be graphs. The $(t-1)$-chromatic Ramsey number, denoted by $r_{t-1}^t(G_1, G_2, \ldots, G_t)$, is defined to be the least number $n$ such that if the edges of the complete graph $K_n$ are colored in any fashion with $t$ colors, then for some $i$ the subgraph whose edges are colored with the $i$th subset of the colors contains $G_i$. In this paper, the authors determine the exact value of $r_4^5(G_1, G_2, \ldots, G_5)$ where each $G_i$ is a path. This verifies a conjecture of \textit{A. Khamseh} and \textit{G. R. Omidi} [Int. J. Comput. Math. 89, No. 10, 1303--1310 (2012; Zbl 1257.05095)].
reviewed by: Baoyindureng Wu
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 6916055
zbMATH Keywords: Ramsey numbers
zbMATH Keywords: $(t-1)$-chromatic Ramsey numbers
zbMATH Keywords: edge coloring
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6916055