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A NOTE ON RAMSEY NUMBERS FOR FANS

Part of: Extremal combinatorics Graph theory

Published online by Cambridge University Press:  13 May 2015

YANBO ZHANG ,
HAJO BROERSMA  and
YAOJUN CHEN
YANBO ZHANG
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
HAJO BROERSMA
Affiliation:
Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
YAOJUN CHEN*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China email yaojunc@nju.edu.cn
*
✉yaojunc@nju.edu.cn
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Abstract

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For two given graphs $G_{1}$ and $G_{2}$, the Ramsey number $R(G_{1},G_{2})$ is the smallest integer $N$ such that, for any graph $G$ of order $N$, either $G$ contains $G_{1}$ as a subgraph or the complement of $G$ contains $G_{2}$ as a subgraph. A fan $F_{l}$ is $l$ triangles sharing exactly one vertex. In this note, it is shown that $R(F_{n},F_{m})=4n+1$ for $n\geq \max \{m^{2}-m/2,11m/2-4\}$.

Keywords

Ramsey numberfangoodness

MSC classification

Primary: 05D10: Ramsey theory
Secondary: 05C70: Factorization, matching, partitioning, covering and packing
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 1 , August 2015 , pp. 19 - 23
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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