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On the combinatorial problems which I would most like to see solved

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References

  1. M. Ajtai, J. Komlós andE. Szemerédi, On infinite Sidon sequences,European J. Comb., to appear.

  2. K. Appel andW. Haken, Every planar map is four colourable,Illinois J. of Math. 21 (1977) 429–490.

    MATH  MathSciNet  Google Scholar 

  3. F. A. Behrend, On sets of integers which contain no three terms in arithmetic progression,Proc. Nat. Acad. Sci. USA 32 (1946) 331–332.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. Berge,Graphs and Hypergraphs, North Holland Publ. Comp. Amsterdam—London 1973.

    MATH  Google Scholar 

  5. B. Bollobás,Extremal Graph Theory, London Math. Soc. Mon. No. 11. 1978.

  6. J. A. Bondy, Reflections on the legitimate deck problem,Lecture Notes in Math.,686, Springer 1977, 1–12

    Article  MathSciNet  Google Scholar 

  7. J. A. Bondy andP. Erdős, Ramsey numbers for cycles in graphs,J. Comb. Theory 14 (1973) 46–54.

    Article  MATH  Google Scholar 

  8. J. A. Bondy andR. L. Hemminger, Graph reconstruction,J. of Graph Theory 1 (1977), 227–268.

    MATH  MathSciNet  Google Scholar 

  9. R. C. Bose, E. T. Parker andS. Shrikhande, Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler’s conjecture,Can. J. Math. 12, 189–203.

  10. W. G. Brown, On graphs that do not contain a Thomsen graph,Canad. Math. Bull. 9 (1966) 281–285.

    MATH  MathSciNet  Google Scholar 

  11. W. G. Brown, P. Erdős andV. T. Sós, Some extremal problems onr-graphs,New Directions in the Theory of Graphs (ed. F. Harary), Academic Press 1973, 53–64.

  12. W. G. Brown, P. Erdős andV. T. Sós, On the existence of triangulated spheres in 3-graphs and related questions,Periodica Math. Hung. 3 (1973) 221–228.

    Article  MATH  Google Scholar 

  13. R. H. Bruck andH. J. Ryser, The nonexistence of certain projective planes,Canad. J. Math. 1 (1949) 88–93.

    MATH  MathSciNet  Google Scholar 

  14. N. G. de Bruijn andP. Erdős, A colour problem for infinite graphs and a problem in theory of relations,Nederl. Akad. Wetensch. Proc. Ser. A 54 (1951) 371–373.

    MATH  Google Scholar 

  15. S. A. Burr, Generalized Ramsey theory for graphs — a survey,Graphs and Combinatorics, Lecture Notes in Math. 406, Springer 1974, 52–75.

    Article  MathSciNet  Google Scholar 

  16. P. A. Catlin, Subgraphs of graphs I,Discrete Math. 10 (1974) 225–233.

    Article  MATH  MathSciNet  Google Scholar 

  17. V. Chvátal, Intersection families of edges in hypergraphs having the hereditary property,Hypergraph Seminar, Lecture Notes in Math. 411, Springer 1972, 61–66.

    Article  Google Scholar 

  18. V. Chvátal, R. L. Graham, H. A. Perold andS. H. Whitesides, Combinatorial designs related to the strong perfect graph conjecture,Discrete Math. 26 (1979) 83–92.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. Dénes andA. D. Keedwell,Latin Squares and their applications, Academic Press, New York 1974.

    MATH  Google Scholar 

  20. G. Dirac, In abstrakten Graphen vorhandene 4-Graphen und ihre Unterteilungen,Math. Nachrichten 22 (1960) 61–85.

    MATH  MathSciNet  Google Scholar 

  21. P. Erdős, Combinatorial problems in geometry and number theory,to appear. See alsoP. Erdős, On some problems of elementary and combinatorial geometry,Annali di Mat. ser. 4,104 (1975) 99–108.

    Article  Google Scholar 

  22. P. Erdős andS. Fajtlowicz, On the conjecture of Hajós,to appear in Combinatorica.

  23. P. Erdős, A. W. Goodman andL. Pósa, The representation of a graph by set intersection,Canad. J. Math. 18 (1966) 106–112.

    MathSciNet  Google Scholar 

  24. P. Erdős andA. Hajnal, Unsolved and solved problems in set theory,Proc. Symp. Pure Math. XXIII. Univ. Calif. Berkeley, A.M.S. 1971, 17–48.

  25. P. Erdős andA. Hajnal, On chromatic number of graphs and set systems,Acta Math. Acad. Sci. Hung. 17 (1966) 61–99.

    Article  Google Scholar 

  26. P. Erdős andA. Hajnal, On complete topological subgraphs of certain graphs,Annales Univ. Sci. Budapest 7 (1969) 193–199.

    Google Scholar 

  27. P. Erdős, A. Hajnal andE. C. Milner, A problem on well ordered sets,Acta Math. Acad. Sci. Hung. 20 (1969) 323–329.

    Article  Google Scholar 

  28. P. Erdős, A. Hajnal andS. Shelah, On some general properties of chromatic numbers,Coll. Math. Soc. J. Bolyai 8,Topics in Topology, North-Holland 1972, 243–255.

    Google Scholar 

  29. P. Erdős, A. Hajnal andE. Szemerédi, On almost bipartite large chromatic graphs,to appear in the volume dedicated to the 60th birthday of A. Kotzig.

  30. P. Erdős andI. Kaplansky, The asymptotic number of Latin rectangles,Amer. J. Math. 69 (1946) 230–236.

    Article  Google Scholar 

  31. P. Erdős andD. Kleitman, Extremal problems among subsets of a set,Discrete Math. 8/3 (1974) 281–294. See alsoG. O. H. Katona, Extremal problems for hypergraphs,Combinatorics (M. Hall and J. H. van Lint, eds.) Math. Centre Amsterdam 1974, 215–244.

    Article  Google Scholar 

  32. P. Erdős andL. Lovász, Problems and results on 3-chromatic hypergraphs and some related questions,Coll. Math. J. Bolyai 10 Infinite and Finite Sets, 1973, 609–617.

    Google Scholar 

  33. P. Erdős, E. C. Milner andR. Rado, Intersection theorems for systems of sets III.Austral. J. Math. 18 (1974) 22–40.

    Google Scholar 

  34. P. Erdős andR. Rado, Intersection theorems for systems of sets,J. London Math. Soc. 35 (1960) 85–90.

    Article  MathSciNet  Google Scholar 

  35. P. Erdős andA. Rényi, On the existence of a factor of degree one of a connected random graph,Acta Math. Acad. Sci. Hung. 17 (1966) 359–379.

    Article  Google Scholar 

  36. P. Erdős, A. Rényi andV. T. Sós, On a problem of graph theory,Studia Sci. Math. Hung. 1 (1966) 215–235.

    Google Scholar 

  37. P. Erdős andM. Simonovits, Some extremal problems in graph theory,Comb. Theory and Appl. (P. Erdős et al. eds.)Coll. Math. Soc. J. Bolyai 4 (1969) 377–390.

    Google Scholar 

  38. P. Erdős andM. Simonovits, An extremal graph problem,Acta Math. Acad. Sci. Hung. 22/3–4 (1971) 275–282.

    Google Scholar 

  39. P. Erdős andM. Simonovits, On a valence problem in extremal graph theory,Discrete Math. 5 (1973) 323–334.

    Article  MathSciNet  Google Scholar 

  40. P. Erdős andM. Simonovits, On the chromatic number of geometric graphs, to appear inArs Combinatoria.

  41. P. Erdős andE. Szemerédi, Combinatorial properties of systems of sets,J. of Comb. Theory A 24 (1978) 308–313.

    Article  Google Scholar 

  42. P. Erdős andP. Turán, On some sequences of integers,J. of London Math. Soc. 11 (1936) 341–363.

    Google Scholar 

  43. P. Erdős andP. Turán, On a problem of Sidon in additive number theory and related problems,J. London Math. Soc. 16 (1941) 212–216.

    Article  MathSciNet  Google Scholar 

  44. R. J. Faudree andR. H. Schelp, All Ramsey numbers for cycles in graphs,Discrete Math. 8 (1974) 313–329.

    Article  MATH  MathSciNet  Google Scholar 

  45. P. Frankl, On families of finite sets no two of which intersect in a singleton,Bull. Austral. Math. Soc. 17 (1977) 125–134.

    MATH  MathSciNet  Google Scholar 

  46. P. Frankl, An intersection problem for finite sets,Acta Math. Acad. Sci. Hung. 30 (1977) 371–373.

    Article  MathSciNet  Google Scholar 

  47. P. Frankl, Extremal problems and coverings of the space,European J. of Comb. 1 (1980),to appear.

  48. H. Fürstenberg, Ergodic behaviour of diagonal measures and a theorem of Szemerédi on arithmetic progressions I–III,J. Analyse Math. 31 (1977) 204–256.

    MathSciNet  Google Scholar 

  49. H. Fürstenberg andY. Katznelson, An ergodic Szemerédi theorem for commuting transformations,J. Analyse Math. 34 (1978) 275–291.

    MathSciNet  Google Scholar 

  50. P. Gács andL. Lovász, Khachian’s Algorithm for linear programming,Math. Progr. Studies, to appear

  51. T. Gallai, On covering of graphs,Theory of Graphs, Proc. Coll. Tihany, Hungary 1968, (P. Erdős and G. Katona, eds.) 231–236.

  52. R. L. Graham, B. Rothschild andJ. Spencer,Ramsey Theory, John Wiley, New York 1980.

    MATH  Google Scholar 

  53. H. Hadwiger, Ungelöste Probleme No. 40,Elemente der Math. 16 (1961) 103–104.

    MathSciNet  Google Scholar 

  54. H. Hadwiger, Über eine Klassifikation der Streckenkomplexe,Vierte Naturforsch. Ges. Zürich 88 (1943) 133–142.

    MathSciNet  Google Scholar 

  55. G. Hajós, Über eine Konstruktion nichtn-färbbarer Graphen,Wiss. Zeitschr. Martin Luther Univ. Halle—Wittenberg A 10 (1961) 116–117.

    Google Scholar 

  56. H. Hanani, The existence and construction of balanced incomplete block designs,Ann. Math. Stat. 32 (1961) 361–386.

    MathSciNet  MATH  Google Scholar 

  57. G. O. H. Katona,unpublished.

  58. L. M. Kelly andW. Moser, On the number of ordinary lines determined byn points,Canad. J. Math. 10 (1958) 210–219.

    MATH  MathSciNet  Google Scholar 

  59. L. G. Khachiyan, A polynomial algorithm in linear programming (in Russian)Doklady Akademii Nauk SSSR,244, (1979), 1093–1096.

    MATH  MathSciNet  Google Scholar 

  60. J. Komlós andE. Szemerédi, Limit distribution for the existence of Hamilton cycles in a random graph,Discrete Math., to appear.

  61. T. Kővári, V. T. Sós andP. Turán, On a problem of Zarankiewicz,Coll. Math. 3 (1954) 50–57.

    Google Scholar 

  62. D. G. Larman andC. A. Rogers, The realization of distances within sets in Euclidean space,Mathematica 19 (1972) 1–24.

    MathSciNet  MATH  Google Scholar 

  63. L. Lovász, Normal hypergraphs and the perfect graph conjecture,Discrete Math. 2 (1972) 253–267.

    Article  MATH  MathSciNet  Google Scholar 

  64. L. Lovász,

  65. W. Mader, Homomorphieeigenschaften und mittlere Kantendichte von Graphen,Math. Annalen 174 (1967) 265–268.

    Article  MATH  MathSciNet  Google Scholar 

  66. U. S. R. Murty, How many magic configurations are there,Amer. Math. Monthly 1978/9, 1001–1002.

  67. U. S. R. Murty,unpublished. SeeL. Caccetta andR. Häggkvist, On diameter critical graphs,Discrete Math. 28 (1979) 223–229.

    MathSciNet  Google Scholar 

  68. J. Paris andL. Harrington, A Mathematical Incompleteness in Peano Arithmetic,Handbook of Math. Logic, North Holland, Amsterdam 1977, 1133–1142.

    Google Scholar 

  69. J. Pelikán, Valency conditions for the existence of certain subgraphs,Theory of Graphs, Proc. Coll. Tihany, Hungary 1968, 251–258.

  70. L. Pósa, Hamiltonian cycles in random graphs,Discrete Math. 14 (1976) 359–364.

    Article  MATH  MathSciNet  Google Scholar 

  71. V. Rödl,to appear.

  72. Vera Rosta, On a Ramsey type problem of J. A. Bondy and P. Erdős I–II,J. Comb. Theory B 15 (1973) 94–105, 105–120.

    Article  MATH  MathSciNet  Google Scholar 

  73. K. F. Roth, On certain sets of integers II,J. of London Math. Soc. 29 (1954) 20–26.

    Article  MATH  Google Scholar 

  74. I. Z. Ruzsa andE. Szemerédi, Triple systems with no six points carrying three triangles,Coll. Math. Soc. J. Bolyai 18 Combinatorics (A. Hajnal and V. T. Sós, eds.) North-Holland 1978, 939–946.

  75. M. Simonovits, Paul Turán*rss influence on graph theory,J. Graph Theory 2 (1977). 102–116.

    MathSciNet  Google Scholar 

  76. M. Simonovits, A method for solving extremal problems in graph theory,Theory of Graphs, Proc. Coll. Tihany, Hungary 1966, 279–319.

  77. J. Spencer, Intersection theorems for systems of sets,Canad. Math. Bull. 20 (1977) 249–254.

    MATH  MathSciNet  Google Scholar 

  78. G. Szekeres, On an extremum problem in the plane,Amer. J. Math. 63 (1941) 208–211.

    Article  MATH  MathSciNet  Google Scholar 

  79. E. Szemerédi, On sets of integers containing nok elements in arithmetic progression,Acta Arithm. 27 (1975) 199–245.

    MATH  Google Scholar 

  80. E. Szemerédi, A. Gyárfás andZs. Tuza, Induced subtrees in graphs of large chromatic number,Discrete Math. 30 (1980) 235–244.

    Article  MATH  MathSciNet  Google Scholar 

  81. P. Turán, On an extremal problem in graph theory (in Hungarian)Mat. Fiz. Lapok 48 (1941) 436–452 and On theory of graphs,Coll. Math. 3 (1954) 19–30.

    MATH  MathSciNet  Google Scholar 

  82. B. L. van der Waerden, Beweis einer Baudetschen Vermutung,Nieuw. Arch. Wisk. 15 (1928) 212–216.

    Google Scholar 

  83. R. M. Wilson, An existence theory for pairwise balanced designs I–II,J. Comb. Theory A 13 (1972) 220–273.

    Article  MATH  Google Scholar 

  84. N. Wormald, A 4-chromatic graph with a special plane drawing,J. Austral. Math. Soc. Ser. A. 28 (1979) 1–8.

    Article  MATH  MathSciNet  Google Scholar 

  85. T. Bang, On matrix functioner som med et numerisk lille deficit viser v. d. Waerdens permanenthypotese,Proc. Scandinavian Congress, Turku 1976

  86. S. Friedland, A lower bound for the permanent of a doubly stochastic matrix,Ann. Math. 110 (1979), 167–176

    Article  MathSciNet  Google Scholar 

  87. B. Grünbaum,Arrangements and Spreads, A. M. S., Providence, R. I. 1972

    MATH  Google Scholar 

  88. T. S. Motzkin, The lines and planes connecting the points of a finite set,Trans. A. M. S. 70 (1951), 451–464.

    Article  MATH  MathSciNet  Google Scholar 

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Erdős, P. On the combinatorial problems which I would most like to see solved. Combinatorica 1, 25–42 (1981). https://doi.org/10.1007/BF02579174

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