Ramsey Number of Hypergraph Paths
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@Article{AAM-34-383,
author = {Liu , Erxiong},
title = {Ramsey Number of Hypergraph Paths},
journal = {Annals of Applied Mathematics},
year = {2022},
volume = {34},
number = {4},
pages = {383--394},
abstract = {
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 $v_1, v_2, · · · , v_{s+n(k−s)}$ such that $\{v_{1+i(k-s)}, \cdots, v_{s+(i+1)(k-s)}\}$ is an edge of $H$ for each $0 ≤ i ≤ n−1.$ In this paper, we prove that $R(P^ {(3s,s)}_n , P^{(3s,s)}_3) = (2n + 1)s + 1$ for $n ≥ 3.$
}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20586.html} }
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 -
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 $v_1, v_2, · · · , v_{s+n(k−s)}$ such that $\{v_{1+i(k-s)}, \cdots, v_{s+(i+1)(k-s)}\}$ is an edge of $H$ for each $0 ≤ i ≤ n−1.$ In this paper, we prove that $R(P^ {(3s,s)}_n , P^{(3s,s)}_3) = (2n + 1)s + 1$ for $n ≥ 3.$
Liu , Erxiong. (2022). Ramsey Number of Hypergraph Paths.
Annals of Applied Mathematics. 34 (4).
383-394.
doi:
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