Some Ramsey Schur Numbers
The Ramsey Schur number $RS(s,t)$ is the smallest $n$ such that every 2-colouring of the edges of $K_n$ with vertices $1,2,\ldots,n$ contains a green $K_s$ or there are vertices $x_1,x_2,\ldots,x_t$ fulfilling the equation $x_1+x_2+\cdots+x_{t-1}=x_t$ and all edges $(x_i,x_j)$ are red. We prove $RS(...
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| Veröffentlicht in: | Combinatorics, probability & computing probability & computing, 2005-01, Vol.14 (1-2), p.25-30 |
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| creator | BODE, JENS-P. GRONAU, HANS-DIETRICH O. F. HARBORTH, HEIKO |
| description | The Ramsey Schur number $RS(s,t)$ is the smallest $n$ such that every 2-colouring of the edges of $K_n$ with vertices $1,2,\ldots,n$ contains a green $K_s$ or there are vertices $x_1,x_2,\ldots,x_t$ fulfilling the equation $x_1+x_2+\cdots+x_{t-1}=x_t$ and all edges $(x_i,x_j)$ are red. We prove $RS(3,3)=11, RS(3,t)=t^2-3$ for $t\equiv1\ (\mbox{mod}\ 6)$ and $t=8$, and $RS(3,t)\geq t^2-3$. |
| doi_str_mv | 10.1017/S0963548304006595 |
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| title | Some Ramsey Schur Numbers |
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