Journal of Prime Research in Mathematics
Vol. 1 (2005), Issue 1, pp. 141 – 146
ISSN: 1817-3462 (Online) 1818-5495 (Print)
ISSN: 1817-3462 (Online) 1818-5495 (Print)
Upper bounds for the size Ramsey numbers for \(P_3\) versus \(C^{t}_{3}\) or \(P_{n}\)
Y. Baskoro
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, 40132 Indonesia.
Y. Nuraeni
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, 40132 Indonesia.
A.A.G. Ngurah
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, 40132 Indonesia.
\(^{1}\)Corresponding Author: s304agung@math.itb.ac.id
Copyright © 2006 E.T. Baskoro, Y. Nuraeni, A.A.G. Ngurah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: December, 2006.
Abstract
In this paper, we derive an upper bound for the size Ramsey number for a path \(P_3\) versus a friendship graph \(C_{3}^{t}\). Furthermore, some minimal Ramsey graph for a combination \((P_{3}, C_{3}^{t}) \)is presented. We also give an upper bound of the size Ramsey number for \(P_3\) versus \(P_n\).
Keywords:
Size Ramsey number, path, friendship graph.