Abstract
We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that the class of acyclic graphs has the Ramsey property and uses the partite construction.
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Acknowledgements
Many thanks to Christian Reiher for many helpful comments as well as for his technical help with the preparation of this manuscript. We also thank Jan Hubička and the referees for helpful remarks.
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Both authors were supported by the grants CE-ITI P202/12/G061 of GAČR and ERC-CZ-STRUCO LL1201.
The second author was also supported by NSF grant DMS 1301698.
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Nešetřil, J., Rödl, V. Ramsey Partial Orders from Acyclic Graphs. Order 35, 293–300 (2018). https://doi.org/10.1007/s11083-017-9433-4
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DOI: https://doi.org/10.1007/s11083-017-9433-4