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Ramsey Partial Orders from Acyclic Graphs

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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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References

  1. Abramson, F.G., Harrington, L.A.: Models without indiscernibles. J. Symbolic Logic 43(3), 572–600 (1978). doi:10.2307/2273534. MR503795

    Article  MathSciNet  MATH  Google Scholar 

  2. Fouché, W.L.: Symmetry and the Ramsey degree of posets. Discrete Math. 167/168, 309–315 (1997). doi:10.1016/S0012-365X(96)00236-1. 15th British Combinatorial Conference (Stirling, 1995). MR1446753

    Article  MathSciNet  MATH  Google Scholar 

  3. Nešetřil, J.: Ramsey classes and homogeneous structures. Comb. Probab. Comput. 14, 171–189 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Nešetřil, J., Rödl, V.: Partitions of finite relational and set systems. J. Combinatorial Theory Ser. A 22(3), 289–312 (1977). MR0437351

    MathSciNet  MATH  Google Scholar 

  5. Nešetřil, J., Rödl, V.: Ramsey classes of set systems. J. Combin. Theory Ser. A 34(2), 183–201 (1983). doi:10.1016/0097-3165(83)90055-9. MR692827

    Article  MathSciNet  MATH  Google Scholar 

  6. Nešetřil, J., Rödl, V.: Combinatorial partitions of finite posets and lattices—Ramsey lattices. Algebra Universalis 19(1), 106–119 (1984). doi:10.1007/BF01191498. MR748915

    Article  MathSciNet  MATH  Google Scholar 

  7. Nešetřil, J., Rödl, V.: The partite construction and Ramsey set systems. Discrete Math. 75(1–3), 327–334 (1989). doi:10.1016/0012-365X(89)90097-6. MR1001405

    MathSciNet  MATH  Google Scholar 

  8. Nešetřil, J., Rödl, V.: Two proofs of the Ramsey property of the class of finite hypergraphs. European J. Combin. 3(4), 347–352 (1982). doi:10.1016/S0195-6698(82)80019-X. MR687733

    Article  MathSciNet  MATH  Google Scholar 

  9. Paoli, M., Trotter Jr., W.T., Walker, J.W.: Graphs and orders in Ramsey theory and in dimension theory. In: Graphs and order (Banff, Alta., 1984), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. MR818500, vol. 147, pp 351–394. Reidel, Dordrecht (1985)

    Google Scholar 

  10. Sokić, M.: Ramsey properties of finite posets. Order 29(1), 1–30 (2012). doi:10.1007/s11083-011-9195-3. MR2948746

    Article  MathSciNet  MATH  Google Scholar 

  11. Sokić, M.: Ramsey property, ultrametric spaces, finite posets, and universal minimal flows. Israel J. Math. 194(2), 609–640 (2013). doi:10.1007/s11856-012-0101-5. MR3047085

    Article  MathSciNet  MATH  Google Scholar 

  12. Solecki, S., Zhao, M.: A Ramsey Theorem for Partial Orders with Linear Extensions. European J. Combin. 60(1), 21–30 (2017). doi:10.1016/j.ejc.2016.08.012

    Article  MathSciNet  MATH  Google Scholar 

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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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Authors and Affiliations

  1. Department of Applied Mathematics and Institute of Theoretical Computer Science, Charles University, 11800, Praha 1, Czech Republic

    Jaroslav Nešetřil

  2. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    Vojtěch Rödl

Authors
  1. Jaroslav Nešetřil
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  2. Vojtěch Rödl
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Corresponding author

Correspondence to Jaroslav Nešetřil.

Additional information

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

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