@inproceedings{Dudek2018ConstructiveRN,
title={Constructive Ramsey Numbers for Loose Hyperpaths},
author={Andrzej Dudek and Andrzej Rucinski},
booktitle={LATIN},
year={2018}
}

For positive integers k and \(\ell \), a k-uniform hypergraph is called a loose path of length \(\ell \), and denoted by \(P_\ell ^{(k)}\), if its vertex set is \(\{v_1, v_2, \ldots , v_{(k-1)\ell +1}\}\) and the edge set is \(\{e_i = \{ v_{(i-1)(k-1)+q} : 1 \le q \le k \},\ i=1,\dots ,\ell \}\), that is, each pair of consecutive edges intersects on a single vertex. Let \(R(P_\ell ^{(k)};r)\) be the multicolor Ramsey number of a loose path that is the minimum n such that every r-edge-coloring… Expand

There is an algorithm such that for every $r$-edge-coloring of the edges of the complete $k$-uniform hypergraph, it finds a monochromatic copy of P_\ell^{(k)}$ in time at most $cn^k$.Expand

The upper bound on the multi-color Ramsey numbers of paths and even cycles is improved and a stability version of the Erdős-Gallai theorem is introduced that may be of independent interest.Expand

It is shown that for sufficiently large n, the following conjecture of Faudree and Schelp is proved: for the three-color Ramsey numbers of paths on n vertices, the number of vertices is n.Expand

It is shown that $5n/2-15/2 \le \hat{R}(P_n) \le 74n$ for $n$ sufficiently large, which improves the previous lower bound and improves the upper bound.Expand

In this paper, we give a brief survey on four problems of Ramsey-type. The first and second problems are concerned about a sequence of numbers. The third one appears in discrete geometry and the… Expand