Multicolor on-line degree Ramsey numbers of trees
type: Item
instance of: scholarly article
title: Multicolor on-line degree Ramsey numbers of trees
zbMATH Open document ID: 1274.05317
author: William B. Kinnersley
author: Douglas B. West
published in: Journal of Combinatorics
publication date: 2013-07-12T00:00:00Z
review text: The \(s\)-color on-line degree Ramsey number of \(G\), denoted \(\dot{R}_\Delta(G;s)\), is the minimum \(k\) such that in any on-line coloring with \(s\) colors on graphs with maximum degree at most \(k\), there is a monochromatic copy of \(G\). It is shown that \(\dot{R}_\Delta(T;s) \leq s(\Delta(T) - 1) + 1\) for every tree \(T\). The inequality is sharp, and for trees with adjacent vertices of maximum degree it is precise. Various upper and lower bounds are given for special trees such as stars and double stars. Also, the on-line degree Ramsey numbers \(\dot{R}_\Delta(G_1, G_2, \dots, G_s)\) where the \(G_i\) are paths and special trees are determined.
reviewed by: Ralph Faudree
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C57
zbMATH DE Number: 6187615
zbMATH Keywords: Ramsey numbers
zbMATH Keywords: degree
zbMATH Keywords: on-line coloring
zbMATH Keywords: trees
MaRDI profile type: Publication
DOI: 10.4310/JOC.2012.V3.N1.A4
description: scientific article; zbMATH DE number 6187615