The Ramsey numbers of fans versus a complete graph of order five
| Main Authors: | Zhang, Yanbo; Nanjing University, Chen, Yaojun; Nanjing University |
|---|---|
| Other Authors: | NSFC under grant numbers 11071115, 11371193 and 11101207, and in part by the Priority Academic Program Development of Jiangsu Higher Education Institutions |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2014
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/48 http://www.ejgta.org/index.php/ejgta/article/view/48/18 |
Daftar Isi:
- For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest integer $N$ such that for any graph $G$ of order $N$, either $G$ contains $F$ or the complement of $G$ contains $H$. Let $F_l$ denote a fan of order $2l+1$, which is $l$ triangles sharing exactly one vertex, and $K_n$ a complete graph of order $n$. Surahmat et al. conjectured that $R(F_l,K_n)=2l(n-1)+1$ for $l\geq n\geq 5$. In this paper, we show that the conjecture is true for n=5.