On the restricted size Ramsey number for P3 versus dense connected graphs

Denny Riama Silaban, Edy Tri Baskoro, Saladin Uttunggadewa

Research output: Contribution to journalArticlepeer-review

Abstract

Let F, Gand H be simple graphs. AgraphF is said a (G, H)-arrowing graph if in any red-blue coloring of edges of F we can find a red G or a blue H. The size Ramsey number of G and H, (Formula presented)(G, H), is the minimum size of F. If the order of F equals to the Ramsey number of G and H, r(G, H), then the minimum size of F is called the restricted size Ramsey number of G and H, r*(G, H). The Ramsey number of G and H, r(G, H), is the minimum order of F. In this paper, we study the restricted size number involving a P3. The value of r*(P3, Kn) has been given by Faudree and Sheehan. Here, we examine r*(P3, H) where H is dense connected graph.

Original languageEnglish
Pages (from-to)383-389
Number of pages7
JournalElectronic Journal of Graph Theory and Applications
Volume8
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • dense connected graph
  • path
  • restricted size Ramsey number
  • size Ramsey number

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