Ramsey numbers for partially-ordered sets
Combinatorics
2016-11-29 v2
Abstract
We present a refinement of Ramsey numbers by considering graphs with a partial ordering on their vertices. This is a natural extension of the ordered Ramsey numbers. We formalize situations in which we can use arbitrary families of partially-ordered sets to form host graphs for Ramsey problems. We explore connections to well studied Tur\'an-type problems in partially-ordered sets, particularly those in the Boolean lattice. We find a strong difference between Ramsey numbers on the Boolean lattice and ordered Ramsey numbers when the partial ordering on the graphs have large antichains.
Cite
@article{arxiv.1512.05261,
title = {Ramsey numbers for partially-ordered sets},
author = {Christopher Cox and Derrick Stolee},
journal= {arXiv preprint arXiv:1512.05261},
year = {2016}
}
Comments
18 pages, 3 figures, 1 table