Geodesic
Ramsey properties of countably infinite partial orderings
Marcia J. Groszek1
1Dartmouth College
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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A partial ordering $\mathbb P$ is chain-Ramsey if, for every natural number $n$ and every coloring of the $n$-element chains from $\mathbb P$ in finitely many colors, there is a monochromatic subordering $\mathbb Q$ isomorphic to $\mathbb P$. Chain-Ramsey partial orderings stratify naturally into levels. We show that a countably infinite partial ordering with finite levels is chain-Ramsey if and only if it is biembeddable with one of a canonical collection of examples constructed from certain edge-Ramsey families of finite bipartite graphs. A similar analysis applies to a large class of countably infinite partial orderings with infinite levels.
DOI : 10.37236/3151
Classification : 05C55, 06A07
Mots-clés : Ramsey theory, partially ordered set, chain-Ramsey, edge-Ramsey

Marcia J. Groszek  1

1 Dartmouth College 
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Marcia J. Groszek. Ramsey properties of countably infinite partial orderings. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/3151

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