, Volume 35, Issue 2, pp 293–300 | Cite as

Ramsey Partial Orders from Acyclic Graphs

  • Jaroslav NešetřilEmail author
  • Vojtěch Rödl


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.


Ramsey classes Order Partite construction 


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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.


  1. 1.
    Abramson, F.G., Harrington, L.A.: Models without indiscernibles. J. Symbolic Logic 43(3), 572–600 (1978). doi: 10.2307/2273534. MR503795MathSciNetCrossRefzbMATHGoogle Scholar
  2. 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). MR1446753MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Nešetřil, J.: Ramsey classes and homogeneous structures. Comb. Probab. Comput. 14, 171–189 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Nešetřil, J., Rödl, V.: Partitions of finite relational and set systems. J. Combinatorial Theory Ser. A 22(3), 289–312 (1977). MR0437351MathSciNetzbMATHGoogle Scholar
  5. 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. MR692827MathSciNetCrossRefzbMATHGoogle Scholar
  6. 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. MR748915MathSciNetCrossRefzbMATHGoogle Scholar
  7. 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. MR1001405MathSciNetzbMATHGoogle Scholar
  8. 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. MR687733MathSciNetCrossRefzbMATHGoogle Scholar
  9. 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. 10.
    Sokić, M.: Ramsey properties of finite posets. Order 29(1), 1–30 (2012). doi: 10.1007/s11083-011-9195-3. MR2948746MathSciNetCrossRefzbMATHGoogle Scholar
  11. 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. MR3047085MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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 MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Institute of Theoretical Computer ScienceCharles UniversityPraha 1Czech Republic
  2. 2.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA

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