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arXiv · 1512.05261

Ramsey numbers for partially-ordered sets

Christopher Cox·Derrick Stolee
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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 Turán-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.

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Christopher Cox, Derrick Stolee. 2016-11-28. Ramsey numbers for partially-ordered sets. https://arxiv.org/abs/1512.05261

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