Restricted size Ramsey number for P 3 versus dense connected graphs of order six

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

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

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 min {v(F): F → (G, H)}, the size Ramsey number r∗(G, H) is min {e(F): F → (G, H)}, and the restricted size Ramsey number r∗(G, H) is min {e(F): F → (G, H), v(F) = r(G, H)}. In 1972, Chvá tal and Harary gave the Ramsey number for P3 versus any graph H with no isolates. In 1983, Harary and Miller started the investigation of the (restricted) size Ramsey number for some pairs of small graphs with order at most four. In 1983, Faudree and Sheehan continued the investigation and summarized the complete results on the (restricted) size Ramsey number for all pairs of small graphs with order at most four. In 1998, Lortz and Mengenser gave both the size Ramsey number and the restricted size Ramsey number for all pairs of small forests with order at most five. Lately, we investigate the restricted size Ramsey number for a path of order three versus all connected graphs of order five. In this work, we continue the investigation on the restricted size Ramsey number for a pair of small graphs. In particularly, for a path of order three versus connected graphs of order six.

Original languageEnglish
Title of host publicationInternational Symposium on Current Progress in Mathematics and Sciences 2016, ISCPMS 2016
Subtitle of host publicationProceedings of the 2nd International Symposium on Current Progress in Mathematics and Sciences 2016
EditorsKiki Ariyanti Sugeng, Djoko Triyono, Terry Mart
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735415362
DOIs
Publication statusPublished - 10 Jul 2017
Event2nd International Symposium on Current Progress in Mathematics and Sciences 2016, ISCPMS 2016 - Depok, Jawa Barat, Indonesia
Duration: 1 Nov 20162 Nov 2016

Publication series

NameAIP Conference Proceedings
Volume1862
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference2nd International Symposium on Current Progress in Mathematics and Sciences 2016, ISCPMS 2016
Country/TerritoryIndonesia
CityDepok, Jawa Barat
Period1/11/162/11/16

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