Restricted size Ramsey number for P 3 versus small paths

Denny Riama Silaban, E. T. Baskoro, Saladin Uttunggadewa

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Citations (Scopus)

Abstract

Let F, G, and H be simple graphs. We say F → (G, H) if for every 2-coloring of the edges of F there exist a monochromatic G or H in F. The Ramsey number r(G, H) is defined as min {|V (F)|: F → (G, H)}, the size Ramsey number r(G, H) is defined as min {|E(F)|: F → (G, H)}, and the restricted size Ramsey number r∗(G, H) is defined as min {|E(F)|: F → (G, H), |V (F)| = r(G, H)}. In this paper we give a lower bound for the restricted size Ramsey number for a path P3 versus Pn. We also give the upper bound and the exact restricted size Ramsey number for some small values of n.

Original languageEnglish
Title of host publicationProceedings of the 7th SEAMS UGM International Conference on Mathematics and Its Applications 2015
Subtitle of host publicationEnhancing the Role of Mathematics in Interdisciplinary Research
EditorsYeni Susanti, Indah Emilia Wijayanti, Fajar Adi Kusumo, Irwan Endrayanto Aluicius
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413542
DOIs
Publication statusPublished - 11 Feb 2016
Event7th SEAMS UGM International Conference on Mathematics and Its Applications: Enhancing the Role of Mathematics in Interdisciplinary Research - Yogyakarta, Indonesia
Duration: 18 Aug 201521 Aug 2015

Publication series

NameAIP Conference Proceedings
Volume1707
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference7th SEAMS UGM International Conference on Mathematics and Its Applications: Enhancing the Role of Mathematics in Interdisciplinary Research
CountryIndonesia
CityYogyakarta
Period18/08/1521/08/15

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