Infinite Combinatorics: From Finite to Infinite

  • Lajos Soukup
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 17)


We investigate the relationship between some theorems in finite combinatorics and their infinite counterparts: given a “finite” result how one can get an “infinite” version of it? We will also analyze the relationship between the proofs of a “finite” theorem and the proof of its “infinite” version.


Span Tree Finite Graph Infinite Graph Edge Disjoint Finite Combinatorics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    R. Aharoni and E. Berger, Menger’s Theorem for Infinite Graphs, J. Graph Theory, 50 (2005), 199–211.CrossRefMathSciNetGoogle Scholar
  2. [2]
    R. Aharoni, E. C. Milner and K. Prikry, Unfriendly partitions of a graph, J. Corn-bin. Theory, Ser. B, 50 (1990), no. 1, 1–10.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    R. Ahlswede, P. L. Erdős and N. Graham, A splitting property of maximal antichains, Combinatorica, 15 (1995), no. 4, 475–480.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    B. Bollobás, Modern graph theory, Graduate Texts in Mathematics, 184, Springer-Verlag (New York, 1998).zbMATHGoogle Scholar
  5. [5]
    V. Chvátal and L. Lovász, Every directed graph has a semi-kernel, Hypergraph Seminar (Proc. First Working Sem., Ohio State Univ., Columbus, Ohio, 1972; dedicated to Arnold Ross), pp. 175. Lecture Notes in Math., Vol. 411, Springer (Berlin, 1974).CrossRefGoogle Scholar
  6. [6]
    E. Dalhaus, D. S. Johnson, C. H. Papadimitriou, P. D. Seymour and M. Yannakakis, The Complexity of Multiway Cuts, Proc. 24th Annual ACM Symp. on Theory of Computing (1992), pp. 241–251.Google Scholar
  7. [7]
    R. Diestel, Graph theory, Third edition. Graduate Texts in Mathematics, 173. Springer-Verlag (Berlin, 2005).zbMATHGoogle Scholar
  8. [8]
    R. Diestel, Directions in Infinite Graph Theory and Combinatorics, Topics in Discrete Mathematics 3, Elsevier — North Holland, 1992.Google Scholar
  9. [9]
    P. Erdős, T. Grünwald and E. Vázsonyi, Végtelen gráfok Euler vonalairól (On Euler lines of infinite graphs, in Hungarian), Mat. Fiz. Lapok, 43 (1936).Google Scholar
  10. [10]
    P. Erdős, T. Grünwald and E. Vázsonyi, Über Euler-Linien unendlicher Graphen, J. Math. Phys., Mass. Inst. Techn., 17 (1938), 59–75.Google Scholar
  11. [11]
    P. L. Erdős, A. Frank and L. A. Székely, Minimum multiway cuts in trees, Discrete Appl. Math., 87 (1998), no. 1–3, 67–75.CrossRefMathSciNetGoogle Scholar
  12. [12]
    P. L. Erdős and L. Soukup, How to split antichains in infinite posets, Combinatorica, 27 (2007), no. 2, 147–161.CrossRefMathSciNetGoogle Scholar
  13. [13]
    P. L. Erdős and L. Soukup, Quasi-kernels and quasi-sinks in infinite graphs, submitted.Google Scholar
  14. [14]
    P. L. Erdős and L. A. Székely, Evolutionary trees: an integer multicommodity max-flow-min-cut theorem, Adv. in Appl. Math., 13 (1992), no. 4, 375–389.CrossRefMathSciNetGoogle Scholar
  15. [15]
    A. Hajnal, Infinite combinatorics, Handbook of combinatorics, Vol. 1,2, 2085–2116, Elsevier (Amsterdam, 1995).Google Scholar
  16. [16]
    A. Hajnal, The chromatic number of the product of two N1-chromatic graphs can be countable, Combinatorica, 5 (1985), no. 2, 137–139.zbMATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    P. Komjáth and V. Totik, Problems and theorems in classical set theory, Problem Books in Mathematics, Springer (New York, 2006).zbMATHGoogle Scholar
  18. [18]
    S. Shelah and E. C. Milner, Graphs with no unfriendly partitions, A tribute to Paul Erdős, Cambridge Univ. Press (Cambridge, 1990), pp. 373–384.Google Scholar
  19. [19]
    L. Soukup, On chromatic number of product of graphs, Comment. Math. Univ. Carolin., 29 (1988), no. 1, 1–12.zbMATHMathSciNetGoogle Scholar

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2008

Authors and Affiliations

  • Lajos Soukup
    • 1
  1. 1.Rényi InstituteBudapestHungary

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