## Publications of Péter Komjáth

117. P. Komjáth, J. Schmerl: Graphs on Euclidean spaces defined using transcendental distances, Mathematika, 58(2012), 1—9. pdf

116. P. Komjáth: Conflict free colorings of nonuniform systems of infinite sets, Acta Math. Hung., 133(2011), 305—310. pdf doi:10.1007/s10474-011-0113-3

115. P. Komjáth, J. Larson, N. Sauer: The quasi order of graphs on an ordinal, Disc. Math., 311(2011), 1451–1460. doi:10.1016/j.disc.2010.12.006, pdf

114. P. Komjáth: The chromatic number of infinite graphs—A survey, Discrete Math., 311(2011), 1448–1450. doi:10.1016/j.disc.2010.11.004. pdf

113. P. Komjáth: The list-chromatic number of infinite graphs defined on Euclidean spaces, Discrete & Computational Geometry, 45(2011), 497–502. pdf
DOI: 10.1007/s00454-009-9228-5. The original publication is available at www.springerlink.com.

112. C. Avart, P. Komjáth, V. Rödl: Metric spaces with point character equal to their size, Comment. Math. Univ. Carolin., 51(2010), 459–467. pdf

111. C. Avart, P. Komjáth, T. Łuczak, V. Rödl: Colorful flowers, Topology Appl., 156(2009), no.7, 1386–1443. pdf

110. P. Komjáth: A note on almost disjoint families, Proc. Amer. Math. Soc., 137(2009), 303–305. pdf Mathscinet

109. P. Komjáth: Shelah's proof of diamond, Annales Univ. Sci. Math., 51(2008), 147–150. dvi, pdf

108. P. Komjáth: An uncountably chromatic triple system. Acta Math. Hung., 121(2008), 79–92. pdf

107. A. Hajnal, P. Komjáth: Obligatory subsystems of triple systems, Acta Math. Hung., 119(2008), 1–13. dvi, pdf, Mathscinet

106. C. Avart, P. Komjáth, T. Łuczak, V. Rödl: Colorful flowers, Electronic Notes in Discrete Mathematics, 31(2008), 255–258.

105. P. Komjáth, V. Totik: Ultrafilters, American Mathematical Monthly, 115(2008), 33–44. pdf

104. P. Komjáth, V. Totik: Problems and Theorems in Set Theory , Springer, 2006.

103. M. Foreman, P. Komjáth: The club guessing ideal (commentary on a theorem of Gitik and Shelah), Journal of Math. Logic, 5(2005), 99–147. pdf

102. P. Komjáth, S. Shelah: Finite subgraphs of uncountably chromatic graphs, Journal of Graph Theory, 49(2005), 28–38. dvi, Mathscinet

101. M. Dzamonja, P. Komjáth, C. Morgan: Wild edge colorings of graphs, Journal of Symbolic Logic, 69(2004), 255–264.

100. P. Komjáth, S. Shelah: A Partition Theorem for Scattered Order Types, Combinatorics, Probablity and Computing, 12(2003), 621–626. pdf

99. P. Komjáth: Five degrees of separation, Proc. of the Amer. Math. Soc., 130(2002), 2413–2417. dvi, ps, Mathscinet

98. P. Komjáth, M. Laczkovich: A combinatorial property of cardinals, Proc. of the Amer. Math. Soc., 130(2002), 1487–1491. dvi

97. P. Komjáth: Subgraph chromatic number, Dimacs Series in Discrete Mathematics and Theoretical Computer Science, 58, Set Theory, The Hajnal Conference (Simon Thomas, editor) 2002, 99–106. pdf

96. P. Komjáth: Some remarks on obligatory subsytems of uncountably chromatic triple systems, Combinatorica, 21(2001), 233–238. dvi, ps

95. P. Komjáth: A Ramsey-style extension of a theorem of Erdős and Hajnal, Fund. Math., 170(2001), 119–122. dvi

94. P. Komjáth: Three clouds may cover the plane, Annals of Pure and Applied Logic, 109 (2001)71–75, dvi, ps

93. P. Komjáth, S. Shelah: Two consistency results on set mappings, Journal of Symbolic Logic 65 (2000), 333–338.

It is consistent that there exists a set mapping f:[ℵ4]4→[ℵ4] with no arbitrarily large finite free subsets. For every natural number n < ω it is consistent that there exists a set mapping f: [ℵn]2→[ℵn] with no infinite free set.

92. P. Komjáth: A theorem on countable ordered sets with an application to universal graphs, Lecture Notes in Logic, 13, Logic Colloquium '98, (ed. Samuel R. Buss, Petr Hájek, Pavel Pudlák), Association for Symbolic Logic, 2000, 296–301.

91. P. Komjáth: Some remarks on the partititon calculus of ordinals, Journal of Symbolic Logic, 64(1999), 436–442.

90. P. Komjáth: Some remarks on universal graphs, Disc. Math., 199(1999), 259–265. dvi

There is a universal countable ⋈-free graph.

89. P. Komjáth: A coloring result for the plane, Journal of Applied Analysis, 5(1999), 113–117.

88. P. Komjáth: Limits of transfinite sequences of Baire-2 functions, Real Analysis Exchange, 24(1998/9), 497–502.

87. P. Komjáth: Distinguishing two partition properties of ω1, Fundamenta Mathematicae, 155(1998), 95–99.

86. A. Hajnal, P. Komjáth: A strongly non-Ramsey order type, Combinatorica, 17(1997), 363–367.

85. Z. Füredi, P. Komjáth: Nonexistence of universal graphs without some trees, Combinatorica, 17(1997), 163–171.

84. P. Komjáth: Two remarks on the coloring number, Journal of Combinatorial Theory (B), 70(1997), 301–305. dvi

If a graph has coloring number n+1 then it contains a subgraph of coloring number n. If a graph has coloring number $$n+1$$ then it contains a subgraph of coloring number $$n$$.

83. Z. Füredi, P. Komjáth: On the existence of countable universal graphs, Journal of Graph Theory, 25(1997), 53–58.

82. P. Komjáth: A strongly non-Ramsey uncountable graph, Fund. Math., 154(1997), 203–205.

81. P. Komjáth: A note on $$\omega_1\to \omega_1$$ functions, Combinatorics, Geometry, and Probability, (ed. B. Bollobás and A. Thomason), Cambridge University Press, 1997, 435–438.

80. P. Komjáth: Set theory: Geometric and Real, in: The Mathematics of Paul Erdős, (ed. R.L.Graham, J. Nesetril), Springer, 1996, vol. II, 460–466.

79. P. Komjáth, S. Shelah: Coloring the finite subsets of an uncountable set, Proceedings of the American Math. Soc., 124(1996), 3501–3505. pdf

78. P. Komjáth, S. Shelah: On Taylor's problem, Acta Math. Hung., 70 (1996), 217–225.

77. F.Galvin, A.Hajnal, P. Komjáth: Edge decompositions of graphs with no large independent sets, Publications de L'Institute Mathématique - Beograd, Nouvelle Serie, 57(71)(1995), 71–80.

76. P. Komjáth: Set mappings on generalized linear continua, Coll. Math., 68(1995), 193–195.

75. P. Komjáth: A note on set mapping with meager images, Studia Sci. Math. Hung., 30(1995), 461–467.

If a set of reals of cardinal at most $$\aleph_2$$ has a Sierpinski type decomposition then that can be obtained from an ordering but this may be false for $$\aleph_3$$.

74. P. Komjáth: A note on minors of uncountable graphs, Mathematical Proceedings of the Cambridge Phil. Soc., 117(1995) 7–9.

For every uncountable cardinal κ there are 2κ graphs of cardinality κ none of them being a minor of any other.

73. P. Komjáth, S. Shelah: Universal graphs without large cliques, J. Comb. Theory, (B), 63(1995), 125–135. pdf

72. P. Komjáth: Ramsey-theory and forcing extensions, Proc. Amer. Math. Soc., 121(1994), 217–219.

71. P. Komjáth, E. C. Milner: On a conjecture of Rödl and Voigt, Journal of Combinatorial Theory, (B), 61(1994), 199–209.

70. P. Komjáth: Partitions of vector spaces, Periodica Math. Hung., 28(1994), 187–193.

69. G. Cherlin, P. Komjáth: There is no universal countable pentagon free graph, Journal of Graph Theory, 18(1994), 337–341.

68. P. Komjáth: A consistency result concerning set mappings, Acta Math. Hung., 64(1994), 93–99. pdf

67. P. Komjáth, S. Shelah: A note on a set mapping problem of Hajnal and Máté, Periodica Math. Hung., 28(1994), 39–42. dvi, pdf

66. P. Komjáth: A decomposition theorem for Rn, Proc. Amer. Math. Soc., 120(1994), 921–927.

Rn has a decomposition into countably many pieces none containing points with rational distance.

65. P. Komjáth, J. Pach: The complexity of a class of infinite graphs, Combinatorica, 14(1994), 121–125.

64. P. Komjáth, S. Shelah: On uniformly antisymmetric functions, Real Analysis Exchange, 19(1993–1994), 218–225. pdf

63. P. Komjáth: Some remarks on second category sets, Coll. Math., 66(1993), 57–62.

62. P. Komjáth A note on large chromatic systems of finite sets, Combinatorics, Paul Erdős is Eighty (Volume 1), Keszthely (Hungary), 1993, 271–275.

It is consistent for every natural number $$n$$ that an uncountably chromatic system of $$n$$-element sets with no two members $$A$$ and $$B$$ with $$|A\cap B|\geq2$$ exists on $$\omega_n$$ and with $$2^{\aleph_0} \geq \aleph_n$$ arbitrary.

61. P. Komjáth, S. Shelah: A consistent partition theorem for infinite graphs, Acta Math. Hung., 61(1993), 115–120.

60. P. Komjáth: Set theoretic constructions in Euclidean spaces, in: New Trends in Discrete and Computational Geometry (J. Pach, ed.), Algorithms and Combinatorics, 10, 1993, Springer-Verlag, 303–325.

59. P. Komjáth: Vector sets with no repeated differences, Coll. Math., 64(1993), 129–134.

58. P. Komjáth: A note on Darboux functions, Real Analysis Exchange, 18(1992–93), 249–252.

57. P. Komjáth: The master coloring, Comptes Rendus Mathématiques de l'Academie des sciences, la Société royale du Canada, 14(1992), 181–182.

56. P. Komjáth: Martin's axiom and spanning trees of infinite graphs, Journal of Combinatorial Theory, (B), 56(1992), 141–144.

55. P. Komjáth: A lattice-point problem of Steinhaus, Quarterly J. of Math., 43(1992), 235–241.

54. P. Komjáth: The chromatic number of some uncountable graphs, Coll. Math. Soc. János Bolyai, 60, Sets, graphs, and numbers, Budapest (Hungary), 1991, 439–444.

53. G. Elekes, A. Hajnal, P. Komjáth: Partition theorems for the power set, Coll. Math. Soc. János Bolyai, 60, Sets, graphs, and numbers, Budapest (Hungary), 1991, 211–217.

52. P. Komjáth, J. Pach: Universal elements and the complexity of certain classes of infinite graphs, Discrete Math., 95(1991), 255–270. pdf

51. P. Komjáth: A second category set with only first category functions, Proc. Amer. Math. Soc., 112(1991), 1129–1136.

50. P. Komjáth:A tetrahedron free decomposition of R3, Bull. London Math. Soc., 23(1991), 116–120.

49. P. Komjáth: A set mapping with no infinite free subsets, Journal of Symbolic Logic, 56(1991), 1400–1402.

It is consistent that there is a set mapping f:[ℵ2]2 →[ℵ2] with no infinite free set.

48. F. Galvin, P. Komjáth: Graph colorings and the axiom of choice, Periodica Math. Hung. 22 (1991), 71–75.

47. P. Komjáth: A Galvin-Hajnal conjecture on infinite graphs, in: A Tribute to P. Erdõs (ed. A. Baker, B. Bollobás, A. Hajnal), Camb. Univ. Press, 1990, 313–316.

46. P. Erdõs, P. Komjáth: Countable decompositions of R2 and R3, Discrete and Computational Geometry, 5(1990), 325–331.

45. P. Komjáth: Ordered families of Baire-2 functions, Real Analysis Exchange, 15 (1989–1990), 442–444.

44. P. Komjáth: Third note on Hajnal-Máté graphs, Studia Sci. Math. Hung., 24(1989) ,403–406.

43. P. Komjáth: On second-category sets, Proc. Amer. Math. Soc., 107(1989), 653–654.

42. P. Komjáth: Set systems with finite chromatic number, European Journal of Combinatorics, 10(1989), 543–549.

41. P. Komjáth, A. Mekler, J. Pach: Some universal graphs, Israel Journal of Mathematics, 64(1988), 158–168. pdf

40. P. Komjáth: Large small sets, Coll. Math., LVI(1988), 231–233.

39. P. Komjáth, S. Shelah: Forcing constructions for uncountably chromatic graphs, Journal of Symbolic Logic, 53(1988), 696–707.

38. P. Komjáth, E. C. Milner, N. Polat: A compactness theorem for perfect matchings in matroids, Journal of Combinatorial Theory, (B), 44(1988), 253–262.

37. P. Komjáth: A simplified construction of nonlinear Davenport-Schinzel sequences, Journal of Combinatorial Theory, (A), 49(1988), 262–267.

36. A. Hajnal, P. Komjáth: Embedding graphs into colored graphs, Trans. Amer. Math. Soc., 307(1988), 395–409. Corrigendum: 332 (1992), 475.

35. P. Komjáth: Consistency results on infinite graphs, Israel Journal of Mathematics, 61(1988), 285–294.

34. A. Hajnal, P. Komjáth, L. Soukup, I. Szalkai: Decompositions of edge colored infinite complete graphs, Coll. Math. Soc. J. Bolyai, 52, Combinatorics, Eger (Hungary), 1987, 277–280.

33. P. Komjáth, W. Weiss: Partitioning topological spaces into countably many pieces, Proc. Amer. Math. Soc., 101(1987), 767–770. pdf

32. R. Aharoni, P. Komjáth: On k-transversals, Journal of Combinatorial Theory, (A), 45(1987), 1–7.

31. P. Komjáth, E. C. Milner: On representing sets of an almost disjoint family of sets, Math. Proc. of the Cambridge Phil. Soc., 101(1987), 385–393.

30. P. Komjáth: Ramsey-type results for metric spaces, Journal of Combinatorial Theory, (A), 45(1987), 323–328.

29. A. Hajnal, P. Komjáth: Some higher-gap examples in combinatorial set theory, Annals of Pure and Applied Logic, 33(1987), 283–296.

28. P. Komjáth: Morasses and the Lévy collapse, Journal of Symbolic Logic, 52(1987), 111–115. pdf.

27. P. Komjáth: The colouring number, Proc. London Math. Soc. 54(1987), 1–14. pdf

26. P. Komjáth: The work of Géza Fodor, Matematikai Lapok, 33(1982–1986), 235–242 (in Hungarian).

25. P. Komjáth: Connectivity and chromatic number of infinite graphs, Israel Journal of Mathematics, 56(1986), 257–266.

24. P. Komjáth: An infinite version of Ryser's inequality, Journal of Combinatorial Theory (A), 43(1986), 329–330.

23. P. Komjáth, V. Rödl: Colorings of universal graphs, Graphs and Combinatorics, 2(1986), 55–60. pdf

22. P. Erdõs, Z. Füredi, A. Hajnal, P. Komjáth, V. Rödl, Á. Seress: Coloring graphs with locally few colors, Discrete Math., 59(1986), 21–34. pdf, doi:10.1016/0012-365X(86)90065-8

21. P. Komjáth: Stationary reflection for uncountable cofinality, Journal of Symbolic Logic, 51(1986), 147–151. pdf

20. P. Komjáth: Comparing almost-disjoint families, Acta Math. Hung., 47(1986), 321–323.

19. P. Komjáth: A second note on Hajnal-Máté graphs, Studia Sci. Math. Hung., 19(1984), 245–246.

18. P. Komjáth: A simple strategy for the Ramsey-game, Studia Sci. Math. Hung., 19(1984), 231–232.

17. P. Komjáth, J. Pach: Universal graphs without large bipartite graphs, Mathematika, 31(1984), 282–290.

16. P. Komjáth, Zs. Szabó: Orientation problems on sequences by recursive functions, Conf. on Automata, Languages, and Mathematical systems, Salgótarján (Hungary), 1984, 129–138.

15. P. Komjáth: On the limit superior of analytic sets, Anal. Math. 10 (1984), 283–293. pdf

14. P. Komjáth: Families close to disjoint ones, Acta Math. Hung. 43 (1984), 199–204. pdf

13. P. Komjáth: A continuous generalization of the transversal property, Math. Proc. Camb. Phil. Soc., 95(1984), 21–23.

12. P. Komjáth: Dense systems of almost disjoint sets, Coll. Math. Soc. J. Bolyai, 37, Finite and Infinite sets , Eger (Hungary), 1981, 527–536.

11. A. Hajnal, P. Komjáth: What must and what need not be contained in a graph of uncountable chromatic number ? Combinatorica 4 (1984), 47-52. pdf

10. P. Komjáth: Almost-disjoint set systems, Candidate Degree Thesis, Budapest, 1983.

9. P. Komjáth: A note on Jensen's covering lemma, Proc. Amer. Math. Soc. 89 (1983), 139–140. pdf

8. P. Komjáth: Large sets not containing images of a given sequence, Canad. Math. Bull. 26 (1983), 41–43.

7. I. Juhász, G. O. H. Katona, P. Komjáth: András Hajnal is 50 years old, Matematikai Lapok, 30(1978–1982), 285–305.

6. J. E. Baumgartner, P. Komjáth: Boolean algebras in which every chain and antichain is countable, Fundamenta Mathematicae CXI (1981), 125-131. pdf, MR 82j:06023

5. P. Komjáth: A note on Hajnal-Máté graphs, Studia Sci. Math. Hung. 15 (1980), 275–276.

4. K. Byleen, P. Komjáth: The admissible trace problem for ℰ-unitary inverse semigroups, Semigroup Forum, 15(1978), 236-246. pdf, MR 57 #16434

3. P. Komjáth: Rearranging transfinite series of ordinals, Bull. Aust. Math. Soc. 16 (1977), 321–323. MR 57 #12232 , On Cambridge Journals

2. P. Komjáth: Constructing almost-disjoint dense set systems, Ph. D. Thesis, Budapest, 1977.

1. G. Hoffmann, P. Komjáth: The transversal property implies property B, Periodica Math. Hung. 7(1976), 179–181. pdf, MR 55 #108

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