Abstract
| Original language | English |
|---|---|
| Place of Publication | Enschede |
| Publisher | University of Twente, Department of Applied Mathematics |
| Number of pages | 9 |
| Publication status | Published - 2002 |
Publication series
| Name | Memorandum |
|---|---|
| Publisher | Department of Applied Mathematics, University of Twente |
| No. | 1621 |
| ISSN (Print) | 0169-2690 |
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Keywords
- MSC-05C55
- IR-65808
- EWI-3441
- MSC-05D10
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The Ramsey numbers of large star-like trees versus large odd wheels. / Surahmat; Baskoro, E.T.; Broersma, H.J.
Enschede : University of Twente, Department of Applied Mathematics, 2002. 9 p. (Memorandum; No. 1621).Research output: Book/Report › Report › Other research output
TY - BOOK
T1 - The Ramsey numbers of large star-like trees versus large odd wheels
AU - Surahmat, null
AU - Baskoro, E.T.
AU - Broersma, H.J.
N1 - Imported from MEMORANDA
PY - 2002
Y1 - 2002
N2 - For two given graphs $G$ and $H$, the \textit{Ramsey number} $R(G,H)$ is the smallest positive integer $N$ such that for every graph $F$ of order $N$ the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we shall study the Ramsey number $R(T_n,W_{m})$ for a star-like tree $T_n$ with $n$ vertices and a wheel $W_m$ with $m+1$ vertices and $m$ odd. We show that the Ramsey number $R(S_{n},W_{m})=3n-2 $ for $n\geq 2m-4, m\geq 5$ and $m$ odd, where $S_n$ denotes the star on $n$ vertices. We conjecture that the Ramsey number is the same for general trees on $n$ vertices, and support this conjecture by proving it for a number of star-like trees.
AB - For two given graphs $G$ and $H$, the \textit{Ramsey number} $R(G,H)$ is the smallest positive integer $N$ such that for every graph $F$ of order $N$ the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we shall study the Ramsey number $R(T_n,W_{m})$ for a star-like tree $T_n$ with $n$ vertices and a wheel $W_m$ with $m+1$ vertices and $m$ odd. We show that the Ramsey number $R(S_{n},W_{m})=3n-2 $ for $n\geq 2m-4, m\geq 5$ and $m$ odd, where $S_n$ denotes the star on $n$ vertices. We conjecture that the Ramsey number is the same for general trees on $n$ vertices, and support this conjecture by proving it for a number of star-like trees.
KW - MSC-05C55
KW - IR-65808
KW - EWI-3441
KW - MSC-05D10
M3 - Report
T3 - Memorandum
BT - The Ramsey numbers of large star-like trees versus large odd wheels
PB - University of Twente, Department of Applied Mathematics
CY - Enschede
ER -