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| RAMSEY NUMBER OF HYPERGRAPH PATHS |
| Erxiong Liu |
| (College of Math. and Computer Science, Fuzhou University, Fuzhou 350116, Fujian, PR China) |
| DOI： |
| Abstract: |
| Let $H=(V,E)$ be a $k$-uniform hypergraph. For $1\leq s\leq k-1$, an $s$-path $P^{(k,s)}_{n}$ of length $n$ in $H$ is a sequence of distinct vertices $v_1,v_2,\cdots,v_{s+n(k-s)}$ such that $\{v_{1+i(k-s)},\cdots, v_{s+(i+1)(k-s)}\}$ is an edge of $H$ for each $0\leq i \leq n-1$. In this paper, we prove that $R(P^{(3s,s)}_{n},P^{(3s,s)}_{3})=(2n+1)s+1$ for $n\ge3$. |
| Key words: hypergraph Ramsey number; path |