On the Ramsey Number of mPn
碩士 === 國立交通大學 === 應用數學系 === 89 === For a fixed graph $G$, we define the smallest integer $r=R(G)$ to be the order of a complete graph $K_{r}$ such that no matter how we assign two colors to the edges of $K_{r}$, there exists a monochromatic subgraph which is isomorphic to $G$....
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| Format: | Others |
| Language: | en_US |
| Published: |
2001
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| Online Access: | http://ndltd.ncl.edu.tw/handle/70643927348783879015 |
| Summary: | 碩士 === 國立交通大學 === 應用數學系 === 89 === For a fixed graph $G$, we define the smallest integer $r=R(G)$ to be the order of a complete graph $K_{r}$ such that no matter how we assign two colors to the edges of $K_{r}$, there exists a
monochromatic subgraph which is isomorphic to $G$. In this
thesis, we show that for $2 \leq n \leq 7$, $R(mP_{n})=m(n+[n/2])-1$ for any $m$.
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