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A many-facetted problem of zarankiewicz

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The Many Facets of Graph Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 110))

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References

  1. L.W. Beineke, Topological aspects of complete graphs, in G. Katona (ed.) Theory of Graphs, Akadémiai Kiadó, Budapest, 1968, 19–26.

    Google Scholar 

  2. E.R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, 1968.

    Google Scholar 

  3. W.G. Brown, On graphs which do not contain a Thomsen graph, Canad. Math. Bull., 9 (1966), 281–285, MR 34 (1967), #81.

    Article  MathSciNet  MATH  Google Scholar 

  4. R.H. Bruck and H.J. Ryser, The non-existence of certain finite projective planes, Canad. J. Math., 1 (1949), 88–93. MR 10 (1949), 319.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Chowla and H.J. Ryser, Combinatorial problems, Canad. J. Math., 2 (1950), 93–99. MR 11 (1950), 306.

    Article  MathSciNet  MATH  Google Scholar 

  6. H.S.M. Coxeter, Regular compound polytopes in more than four dimensions, J. Math. and Phys., 12 (1932–3), 334–345.

    Article  MATH  Google Scholar 

  7. K. Culik, Poznámka k problému K. Zarankiewicze, Pracé Brnenské Základny CSAV, 26 (1955), 341–348.

    MathSciNet  Google Scholar 

  8. K. Culik, Teilweise Lösung eines verallgemeinerten Problem von K. Zarankiewicz, Ann. Polon. Math., 3 (1956), 165–168. MR 18 (1957), 459.

    MathSciNet  MATH  Google Scholar 

  9. P. Erdös, Extremal problems in graph theory, in M. Fiedler (ed.), Theory of Graphs and its Applications (Proc. Symp. Smolenice, (1963), Prague, 1964, 29–36. MR 31 (1966), #4735.

    Google Scholar 

  10. P. Erdös, Some applications of probability to graph theory and combinatorial problems, in M. Fiedler (ed.), Theory of Graphs and its Applications (Proc. Symp. Smolenice, 1963), Prague, 1964, 29–36, MR 30 (1965), #3459.

    Google Scholar 

  11. P. Erdös, On extremal problems of graphs and generalized graphs, Israel J. Math., 2 (1964), 183–190. MR 32 (1966), #1134.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Erdös and R. Rado, A partition calculus in set theory, Bull. Amer. Math. Soc., 62 (1956), 427–489. MR 18 (1957), 458.

    Article  MathSciNet  MATH  Google Scholar 

  13. P. Erdös and R. Rado, A combinatorial theorem, J. London Math. Soc., 25 (1950), 249–255. MR 13 (1952), 322.

    Article  MathSciNet  MATH  Google Scholar 

  14. P. Erdös and G. Szekeres, A combinatorial problem in geometry, Compositio Math., 2 (1935), 463–470.

    MathSciNet  MATH  Google Scholar 

  15. M.K. Fort, Jr. and G.A. Hedlund, Minimal coverings of pairs by triples, Pacific J. Math., 8 (1958), 709–719. MR 21 (1960), #2595.

    Article  MathSciNet  MATH  Google Scholar 

  16. R.K. Guy, A coarseness conjecture of Erdös, J. Combinatorial Theory, 3 (1967), 38–42. MR 35 (1968), #78.

    Article  MathSciNet  MATH  Google Scholar 

  17. R.K. Guy, A problem of Zarankiewicz, in G. Katona (ed.), Theory of Graphs, Akadémiai Kiadó, Budapest, 1968, 119–150.

    Google Scholar 

  18. R.K. Guy and L.W. Beineke, The coarseness of the complete graph, Canad. J. Math., 20 (1968), 888–894. MR 37 (1969), #2633.

    Article  MathSciNet  MATH  Google Scholar 

  19. R.K. Guy and S. Znám, A problem of Zarankiewicz, in W.T. Tutte (ed.), Recent Progress in Combinatorics, Academic Press, 1969.

    Google Scholar 

  20. M. Hall, Cyclic projective planes, Duke Math. J., 14 (1947), 1079–1090. MR 9 (1948), 370.

    Article  MathSciNet  MATH  Google Scholar 

  21. M. Hall, Automorphisms of Steiner triple systems, I.B.M. J. Res. Develop., 4 (1960), 460–472, MR 23 (1962), #A1282.

    MathSciNet  MATH  Google Scholar 

  22. M. Hall, Combinatorial Theory, Blaisdell, 1967. MR 37 (1969), #80.

    Google Scholar 

  23. M. Hall and H.J. Ryser, Cyclic incidence matrices, Canad. J. Math., 3 (1951), 495–502. MR 13 (1952), 312.

    Article  MathSciNet  MATH  Google Scholar 

  24. H. Hanani, A note on Steiner triple systems, Math. Scand., 8 (1960), 154–156. MR 23 (1962), #A2330.

    MathSciNet  MATH  Google Scholar 

  25. H. Hanani, On quadruple systems, Canad. J. Math., 12 (1960), 145–157, MR 22 (1961), #2558.

    Article  MathSciNet  MATH  Google Scholar 

  26. H. Hanani, The existence and construction of balanced incomplete designs, Ann. Math. Statist., 32 (1961), 361–386. MR 29 (1965), #4161.

    Article  MathSciNet  MATH  Google Scholar 

  27. H. Hanani, On some tactical configurations, Canad. J. Math., 15 (1963), 702–722. MR 28 (1964), #1136.

    Article  MathSciNet  MATH  Google Scholar 

  28. H. Hanani and J. Schönheim, On Steiner systems, Israel J. Math., 2 (1964), 139–142. MR 31 (1966), #73. Addendum, ibid., 4 (1966), 144. MR 34 (1967), #72.

    Article  MathSciNet  MATH  Google Scholar 

  29. S. Hartman, J. Mycielski, and C. Ryll-Nardzewski, Collog. Math., 3 (1954), 84–85.

    Google Scholar 

  30. A.J. Hoffman, Cyclic affine planes, Canad. J. Math., 4 (1952), 295–301. MR 14 (1953), 196.

    Article  MathSciNet  MATH  Google Scholar 

  31. C. Hylteń-Cavallius, On a combinatorical problem, Collog. Math., 6 (1958), 59–65. MR 21 (1960), #1941.

    MathSciNet  MATH  Google Scholar 

  32. T.P. Kirkman, On triads made with fifteen things, London Edinburgh and Dublin Phil. Mag., 37 (1850), 169–171.

    Google Scholar 

  33. T.P. Kirkman, On the puzzle of the fifteen young ladies, London Edinburgh and Dublin Phil. Mag., (4), 23 (1862), 198–204.

    Google Scholar 

  34. A. Kotzig, Cycles in a complete graph oriented in equilibrium, Mat. Fyz. Casopis, 16 (1966), 175–182. MR 34 (1967), #2491.

    MathSciNet  MATH  Google Scholar 

  35. A. Kotzig, Des cycles dans les tournois, in P. Rosenstiehl (ed.), Théorie des Graphes, (Symp. Rome, 1966), Dunod, Paris, 1967, 203–208.

    Google Scholar 

  36. T. Kövári, V. Sós, and P. Turán, On a problem of K. Zarankiewicz, Colloq. Math., 3 (1954), 50–57. MR 16 (1955), 456.

    MathSciNet  MATH  Google Scholar 

  37. E. Lehmer, On residue difference sets, Canad. J. Math., 5 (1953), 425–432. MR 15 (1954), 10.

    Article  MathSciNet  MATH  Google Scholar 

  38. E.H. Moore, Concerning triple systems, Math. Ann., 43 (1893), 271–285.

    Article  MathSciNet  MATH  Google Scholar 

  39. E. Netto, Lehrbuch der Combinatorik, Leipzig, 1927, Chelsea, 1958. MR 20 (1959), #1632.

    Google Scholar 

  40. R.E.A.C. Paley, On orthogonal matrices, J. Math. and Phys., 12 (1933), 311–320.

    Article  MATH  Google Scholar 

  41. F.P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. (2), 30 (1930), 264–286.

    Article  MathSciNet  MATH  Google Scholar 

  42. D.K. Ray-Chaudhuri and R.M. Wilson, Solution of Kirkman's school-girl problem, Proc. Amer. Math. Soc. Symp. on Combinatorics, Los Angeles, 1968.

    Google Scholar 

  43. I. Reiman, Uber ein Problem von K. Zarankiewicz, Acta Math. Acad. Sci. Hungar., 9 (1958), 269–279. MR 21 (1960), #63.

    Article  MathSciNet  MATH  Google Scholar 

  44. M. Reiss, Ueber eine Steinersche combinatorische Aufgabe welche in 45-sten Bande dieses Journals, Seite 181, gestellt worden ist, J. Reine Angew. Math., 56 (1859), 326–344.

    Article  MathSciNet  Google Scholar 

  45. G. Ringel, Die toroidale Dicke des vollständigen Graphen, Math. Z., 87 (1965), 19–26. MR 30 (1965), #2489.

    Article  MathSciNet  MATH  Google Scholar 

  46. H.J. Ryser, Combinatorial Mathematics, Carus Monograph #14, Math. Assoc. Amer. 1963. MR 27 (1964), #51.

    Google Scholar 

  47. J. Schönheim, On coverings, Pacific J. Math., 14 (1964), 1405–1411, MR 30 (1965), #1954.

    Article  MathSciNet  MATH  Google Scholar 

  48. J. Schönheim, On maximal systems of k-tuples, Studia Sci. Math. Hungar., 1 (1966), 363–368. MR 34 (1967), #2485.

    MathSciNet  MATH  Google Scholar 

  49. J. Schönheim, On linear and non-linear simple error-correcting q-nary perfect codes, Information and Control, 12 (1968), 23–26.

    Article  MathSciNet  MATH  Google Scholar 

  50. W. Sierpiński, Sur un probléme concernant un réseau a 36 points, Ann. Polon. Math., 24 (1951), 173–174. MR 15 (1954), 594.

    MATH  Google Scholar 

  51. W. Sierpiński, Problems in the Theory of Numbers (trans. A. Sharma), Pergamon, 1964, 16. MR 30 (1965), #1078.

    Google Scholar 

  52. J. Singer, A theorem in finite projective geometry and some applications to number theory, Trans. Amer. Math. Soc., 43 (1938), 377–385.

    Article  MathSciNet  MATH  Google Scholar 

  53. T. Skolem, Some remarks on the triple systems of Steiner, Math. Scand., 6 (1958), 273–280. MR 21 (1960), #5582.

    MathSciNet  MATH  Google Scholar 

  54. J. Steiner, Combinatorische Aufgabe, J. Reine Angew. Math., 45 (1853), 181–182.

    Article  MathSciNet  Google Scholar 

  55. T. Storer, Cyclotomy and Difference Sets, Markham, 1967. MR 36 (1968), #128.

    Google Scholar 

  56. J.A. Todd, A combinatorial problem, J. Math. and Phys., 12 (1933), 321–333.

    Article  MATH  Google Scholar 

  57. P. Turán, Eine Extremalaufgabe aus der Graphentheorie, Mat. Fiz. Lapok, 48 (1941), 436–452. MR 8 (1947), 284.

    MathSciNet  MATH  Google Scholar 

  58. P. Turán, On the theory of graphs, Colloq. Math., 3 (1954), 19–30.

    MATH  Google Scholar 

  59. K. Zarankiewicz, Problem P101, Colloq. Math., 2 (1951), 301.

    Google Scholar 

  60. S. Znám, On a combinatorical problem of K. Zarankiewicz, Colloq. Math., 11 (1963), 81–84. MR 29 (1965), #37.

    MathSciNet  MATH  Google Scholar 

  61. S. Znám, Two improvements of a result concerning a problem of K. Zarankiewicz, Colloq. Math., 13 (1965), 255–258. MR 32 (1966), #7434.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. University of Calgary, Canada

    Richard K. Guy

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  1. Richard K. Guy
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G. Chartrand S. F. Kapoor

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© 1969 Springer-Verlag

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Guy, R.K. (1969). A many-facetted problem of zarankiewicz. In: Chartrand, G., Kapoor, S.F. (eds) The Many Facets of Graph Theory. Lecture Notes in Mathematics, vol 110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060112

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  • DOI: https://doi.org/10.1007/BFb0060112

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  • Print ISBN: 978-3-540-04629-5

  • Online ISBN: 978-3-540-36161-9

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