# Constructive Ramsey Numbers for Loose Hyperpaths

@inproceedings{Dudek2018ConstructiveRN,
title={Constructive Ramsey Numbers for Loose Hyperpaths},
author={Andrzej Dudek and Andrzej Rucinski},
booktitle={LATIN},
year={2018}
}
• Published in LATIN 16 April 2018
• Mathematics
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…
1 Citations
Monochromatic loose paths in multicolored k-uniform cliques
• Mathematics
Discret. Math. Theor. Comput. Sci.
• 2019
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$. ## References SHOWING 1-9 OF 9 REFERENCES On the Multi-Colored Ramsey Numbers of Paths and Even Cycles 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. Three-color Ramsey numbers for paths • Mathematics Comb. • 2008 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. On some Multicolor Ramsey Properties of Random Graphs • Mathematics SIAM J. Discret. Math. • 2017 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.
The Ramsey number for a triple of long even cycles
• Mathematics
J. Comb. Theory, Ser. B
• 2007
On Ramsey-Type Problems
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