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 $G$....
Main Authors: | , |
---|---|
Other Authors: | |
Format: | Others |
Language: | en_US |
Published: |
2001
|
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 $m$.
|
---|