Ramsey Partial Orders from Acyclic Graphs
Jaroslav Ne\v{s}et\v{r}il, Vojt\v{e}ch R\"odl
TL;DR
This paper proves that finite partial orders with a linear extension form a Ramsey class by leveraging the Ramsey property of acyclic graphs and employing the partite construction method.
Contribution
It establishes the Ramsey property for a new class of finite partial orders with linear extensions, expanding the understanding of Ramsey classes.
Findings
Finite partial orders with linear extensions form a Ramsey class.
The proof utilizes the Ramsey property of acyclic graphs.
The partite construction is key to the proof.
Abstract
We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that class of acyclic graphs has the Ramsey property and uses the partite construction.
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