Ramsey Classes with Closure Operations (Selected Combinatorial Applications)
Abstract
We state the Ramsey property of classes of ordered structures with closures and given local properties. This generalises many old and new results: the Ne\v{s}et\v{r}il-R\"{o}dl Theorem, the author's Ramsey lift of bowtie-free graphs as well as the Ramsey Theorem for Finite Models (i.e. structures with both functions and relations) thus providing the ultimate generalisation of Structural Ramsey Theorem. We give here a more concise reformulation of recent authors paper "All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)" and the main purpose of this paper is to show several applications. Particularly we prove the Ramsey property of ordered sets with equivalences on the power set, Ramsey theorem for Steiner systems, Ramsey theorem for resolvable designs and a partial Ramsey type results for -factorizable graphs. All of these results are natural, easy to state, yet proofs involve most of the theory developed.
Cite
@article{arxiv.1705.01924,
title = {Ramsey Classes with Closure Operations (Selected Combinatorial Applications)},
author = {Jan Hubička and Jaroslav Nešetřil},
journal= {arXiv preprint arXiv:1705.01924},
year = {2017}
}
Comments
16 pages, 2 figures. Minor correction according to referees comments. arXiv admin note: text overlap with arXiv:1606.07979. Author note: main theorem of arXiv:1606.07979 is used here