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| THE BOUNDS ABOUT THE WHEEL-WHEEL RAMSEY NUMBERS |
| Lili Shen,Xianzhang Wu |
| (College of Math. and Computer Science, Fuzhou University, Fuzhou 350116, Fujian, PR China) |
| DOI： |
| Abstract: |
| In this paper, we determine the bounds about Ramsey number $R(W_m, W_n)$, where $W_i$ is a graph obtained from a cycle $C_i$ and an additional vertex by joining it to every vertex of the cycle $C_i$. We prove that $3m+1\leq R(W_m,W_n)\leq 8m-3$ for odd $n$, $m\geq n\geq3$, $m\geq 5,$ and $2m+1\leq R(W_m,W_n)\leq 7m-2$ for even $n$ and $m\geq n+502$. Especially, if $m$ is sufficiently large and $n=3$, we have $R(W_m,W_3)= 3m+1.$ |
| Key words: Ramsey number; wheel; bounds |