Ramsey numbers for the path with three edges
type: Item
instance of: scholarly article
title: Ramsey numbers for the path with three edges
zbMATH Open document ID: 0606.05046
DOI: 10.1016/S0195-6698(86)80022-1
published in: European Journal of Combinatorics
publication date: 1986-01-01T00:00:00Z
review text: Let k be a natural number and let \(P_ 3\) denote the path with three edges. The Ramsey number \(r(P_ 3,k)\) is the minimum number of vertices in a complete graph for which every k-coloring admits a monochromatic copy of \(P_ 3\). The Ramsey number \(r(F_ 3,k)\) is the minimum number of vertices in a complete graph for which every k-coloring admits a monochromatic connected subgraph or more than three vertices. This note contains the following two \(results:\) r(P\({}_ 3,k)=2k+2\), if \(k\equiv (mod 3)\), \(r(P_ 3,k)=2k+1\), if \(k\equiv 0\) or 2(mod 3), \(k\neq 3\), \(r(P_ 3,k)=6\), if \(k=3,\) r(F\({}_ 3,k)=2k+2\), if \(k\equiv 1(mod 3)\), \(r(F_ 3,k)=2k\), if \(k=3\) or \(k\equiv 2(mod 3)\), \(r(F_ 3,k)=2k+1\) if \(k=3^ mh>3\), \(h\in 1(mod 3)\).
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 3979104
zbMATH Keywords: path
zbMATH Keywords: Ramsey number
author: Jürgen Bierbrauer
reviewed by: Jack E. Graver
MaRDI profile type: Publication
cites work: On generalized Ramsey numbers for trees
cites work: Generalised Ramsey numbers for small graphs
cites work: Undecided Ramsey-numbers for paths
cites work: On reverse Steiner triple systems
cites work: Q4744276
full work available at URL: s0195-6698(86)80022-1
OpenAlex ID: W2317574491
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description: scientific article; zbMATH DE number 3979104