TY - JOUR
T1 - Ramsey Number of Hypergraph Paths
AU - Liu , Erxiong
JO - Annals of Applied Mathematics
VL - 4
SP - 383
EP - 394
PY - 2022
DA - 2022/06
SN - 34
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20586.html
KW - hypergraph Ramsey number, path.
AB - <p style="text-align: justify;">Let $H = (V, E)$ be a $k$-uniform hypergraph. For $1 ≤ s ≤ k − 1,$ an $s$-path $P^{(k,s)}_n$ of length $n$ in $H$ is a sequence of distinct vertices&nbsp;<span style="text-align: justify;">$v_1, v_2, · · · , v_{s+n(k−s)}$</span> such that $\{v_{1+i(k-s)}, \cdots, v_{s+(i+1)(k-s)}\}$ is an edge of $H$ for each $0 ≤ i ≤ n−1.$ In this paper, we prove that $R(P^ {(3s,s)}_n , P^{(3s,s)}_3) = (2n + 1)s + 1$ for $n ≥ 3.$</p>