The Ramsey Numbers of Paths Versus Fans

M. Salman

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Abstract

For two given graphs G and H, the Ramsey number R(G,H) is the smallest positive integer p such that for every graph F on p vertices the following holds: either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we study the Ramsey numbers R(Pn,Fm), where Pn is a path on n vertices and Fm is the graph obtained from m disjoint triangles by identifying precisely one vertex of every triangle (Fm is the join of K1 and mK2). We determine exact values for R(Pn,Fm) for the following values of n and m: n = 1,2 or 3 and m ≥ 2; n ≥ 4 and 2 ≤ m ≤ (n + 1)/2; n ≥ 7 and m = n − 1 or m = n; n ≥ 8 and (k · n − 2k + 1)/2 ≤ m ≤ (k · n − k + 2)/2 with 3 ≤ k ≤ n − 5; n = 4,5 or 6 and m ≥ n − 1; n ≥ 7 and m ≥ (n − 3)2/2.
Original languageUndefined
Title of host publication2nd Cologne-Twente Workshop on Graphs and Combinatorial Optimization
EditorsHaitze J. Broersma, U. Faigle, Johann L. Hurink, Stefan Pickl, Gerhard Woeginger
PublisherElsevier
Pages103-107
DOIs
Publication statusPublished - 2003
Event2nd Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2003 - University of Twente, Enschede, Netherlands
Duration: 14 May 200316 May 2003

Publication series

NameElectronic Notes in Discrete Mathematics
PublisherElsevier
Volume13

Workshop

Workshop2nd Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2003
Abbreviated titleCTW
CountryNetherlands
CityEnschede
Period14/05/0316/05/03

Keywords

  • Path
  • IR-74946
  • Fan
  • Ramsey number

Cite this

Salman, M. (2003). The Ramsey Numbers of Paths Versus Fans. In H. J. Broersma, U. Faigle, J. L. Hurink, S. Pickl, & G. Woeginger (Eds.), 2nd Cologne-Twente Workshop on Graphs and Combinatorial Optimization (pp. 103-107). (Electronic Notes in Discrete Mathematics; Vol. 13). Elsevier. https://doi.org/10.1016/S1571-0653(04)00448-2