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Publications of Prof. Nedialko Nenov, Dr. Habil


 

  1. New upper bound for a class of vertex Folkman numbers. (with Kolev, N.), Electron. J. Combin. 13 (2006), #R14.

  2. Folkman number Fe(3, 4; 8) is equal to 16. (with Kolev, N.) C. R. Acad. Bulg. Sci. 59 (2006), № 1, 25-30.

  3. Improvement of graph theory Wei's inequality. Mathematics and Education. Proc. Thirty Fifth Spring Conf. Union Bulg. Math., Borovets, 2006, 191-194.

  4. New recurrent inequality on a class of vertex Folkman numbers. (with Kolev, N.) Mathematics and Education. Proc. Thirty Fifth Spring Conf. Union Bulg. Math., Borovets, 2006, 164-168.

  5. Extremal problems of graph colorings. Dr. Sci. Thesis, Sofia Univ., Sofia, 2005.

  6. An example of a 16-vertex Folkman (3, 4)-graph without 8-cliques. (with Kolev, N.) to appear in Annuaire Univ. Sofia, Fac. Math. Inform. 98 (2005).

  7. On the 2-coloring diagonal vertex Folkman numbers with minimal possible clique number. (with Kolev, N.) to appear in Annuaire Univ. Sofia, Fac. Math. Inform. 98 (2005).

  8. Balanced vertex sets in graphs. (with Khadzhiivanov, N.) Annuaire Univ. Sofia Fac. Math. Inform. 97 (2005), 50-64.
  9. Turan's Theorem and maximal degrees. (with Khadzhiivanov, N.) Annuaire Univ. Sofia Fac. Math. Inform. 96 (2004), 173-174.
  10. Sequences of maximal degree vertices in graphs. (with Khadzhiivanov, N.) Serdica Math. J. 30 (2004), 96-102.
  11. Saturated β-sequences in graphs. (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 57 (2004), n. 6, 49-54.
  12. Lower bounds for some Ramsey numbers. Annuaire Univ. Sofia Fac. Math. Inform. 96 (2004), 85-87.
  13. Generalized Turan's graphs theorem. (with Khadzhiivanov, N.) Annuaire Univ. Sofia Fac. Math. Inform. 96 (2004), 69-73.
  14. Generalized r-partite graphs and Turan's Theorem. (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 57 (2004), n. 2, 19-24.
  15. Bounds on the vertex Folkman numbers F(4, 4; 5). Annuaire Univ. Sofia Fac. Math. Inform. 96 (2004), 75-83.
  16. On the triangle vertex Folkman numbers. Discrete mathematics 271 (2003), 327-334.
  17. On a class of vertex Folkman numbers. Serdica Math. J. 28 (2002), 219-232.
  18. Lower bound for a number of vertices of some vertex Folkman graphs, C. R. Acad. Bulg. Sci. 55 (2002), n. 4, 33-36.
  19. Computation of the vertex Folkman numbers F(2, 2, 2, 4; 6) and F(2, 3, 4; 6). (with Nedialkov, E.) Electron. J. Combin. 9 (2002), #R9.
  20. On the vertex Folkman number F(3, 4). C. R. Acad. Bulg. Sci., 54 (2001), n. 2, 23-26.
  21. On the 3-coloring vertex Folkman number F(2, 2, 4). Serdica Math. J. 27 (2001), 131-136.
  22. Computation of the vertex Folkman numbers F(2, 2, 2, 3; 5) and F(2, 3, 3; 5). Annuaire Univ. Sofia Fac. Math. Inform. 95 (2001), 71-82.
  23. Computation of the vertex Folkman number F(4, 4; 6). (with Nedialkov, E.) Proceedings of the Third Euro Workshop on Optimal Codes and related topics, Sunny Beach, Bulgaria, 11-16 June 2001, 123-128.
  24. A generalization of a result of Dirac. Annuaire Univ. Sofia Fac. Math. Inform. 95 (2001), 59-69.
  25. On the number of independence of a class of graphs. (with Nedialkov, E.) C. R. Acad. Bulg. Sci. 53 (2000), n. 3, 21-24.
  26. On a class of vertex Folkman graphs. Annuaire Univ. Sofia Fac. Math. Inform. 94 (2000), 15-25.
  27. On the small graphs with chromatic number 5 without 4-cliques. Discrete Math 188 (1998), 297-298.
  28. Each 11-vertex graph without 4-cliques has a triangle-free 2 partition of vertices. (with Nedialkov, E.) Annuaire Univ. Sofia Fac. Math. Inform. 91 (1997), 127-147.
  29. Lower bounds for the number of vertices of some Ramsey graphs. (in Russian) Annuaire Univ. Sofia Fac. Math. Inform. 86 (1992), 11-15.
  30. On the (3, 4)-Ramsay graphs without 9-cliques. (in Russian) God. Sofij. Univ., Fak. Mat. Infor. 85 (1993), n. 1 (Math.), 71-81 (1991).
  31. Any 14-vertex graph with a unique triangle has no fewer than five 5-anticliques. (in Russian) (with Khadzhiivanov, N., Pashov, I.) Serdica 13 (1987), 199-209 05C55.
  32. The minimum number of monochromatic 4-cliques for noncovering 2-colorings of the edges of a complete graph. (in Russian) (with Khadzhiivanov, N.) Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat. 22 (1986), 137-149.
  33. The minimum number of 5-anticliques of 14-vertex graphs with two 3-cliques is three. (in Russian) (with Khadzhiivanov, N., Pashov, I.) Godishnik Vissh. Ped. Inst. Shuman Prirod.-Mat. Fak. 1986 (1986), 23-37.
  34. On colorings of edges of complete graphs where the monochromatic triangles do not cover the set of all vertices. (in Russian) (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 39 (1986), n. 6, 31-34.
  35. Erratum: "Any Ramsey graph without 5-cliques has more than 11 vertices". (in Russian) (with Khadzhiivanov, N.) Serdica 12 (1986), 204-204.
  36. Relations and graphs. (in Bulgarian) (with Khadzhiivanov, N.) Fiz.-Mat. Spis. Bulg. Akad. Nauk. 27, (1985), 314-318.
  37. On two-colorings of the edges of complete graphs with a minimal number of monochromatic triangles. (in Russian) (with Khadzhiivanov, N.) Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat. 21 (1985), 181-188.
  38. On the minimum of the number of 3-anticliques in n-vertex graphs without 3-cliques. (in Russian) (with Khadzhiivanov, N.) Serdica 11 (1985), 251-258.
  39. Application of the corona-product of two graphs in Ramsey theory. (in Russian) Annuaire Univ. Sofia Fac. Math. Inform. 79 (1985), 349-355.
  40. Any Ramsey graph without 5-cliques has more than 11 vertices, (in Russian) (with Khadzhiivanov, N.) Serdica 11 (1985), 3341-356.
  41. A problem of Erdös and Hajnak in Ramsey theory. (in Bulgarian) Annuaire Univ. Sofia Fac. Math. Inform. 79 (1985), 5-13.
  42. The number of 5-vertex independent sets of 13-vertex graphs without triangles (in Russian) (with Khadzhiivanov, N.) Serdica 10 (1984), 357-366.
  43. The existence and uniqueness of a 14-vertex graph with three 3-cliques and one 5-anticlique. (in Russian) (with Pashov I., Khadzhiivanov, N.) Annuaire Univ. Sofia Fac. Math. Mech. 78 (1984), 40-55.
  44. The chromatic number of any 10-vertex graph without 4-cliques is at most 4. (in Russian) C. R. Acad. Bulg. Sci. 37 (1984), 301-304.
  45. On the relation of p-non-adjacency on graphs. (in Russian) (with Khadzhiivanov, N.) God. Sofij. Univ., Fak. Mat. Mekh. 78 (1984), n. 1, 68-72 (1988).
  46. On the number of triples of nonacquaintances at a party without triples of acquaintances (in Bulgarian) (with Khadzhiivanov, N.) Fiz.-Mat. Spis. Bulg. Akad. Nauk. 26 (1984), 360-365.
  47. On the number of 3-cliques in some graphs without 4-anticliques. (with Khadzhiivanov, N., Pashov I.) Godishnik Vissh, Ped. Inst. Shuman - Mat. Fak. vol. 8 (1984), 11-29.
  48. On the 4-cliques of some graphs without triangles. (in Russian) (with Khadzhiivanov, N.) Annuaire Univ. Sofia Fac. Math. Mech. 78 (1984), 186-208.
  49. On a Ramsey type property for the 10 vertices graphs. (in Bulgarian with English summary) Mathematics and education in mathematics, Proc. 13th Spring Conf. Union Bulg. Math., Sunny Beach, 1984, 165-172, (1984).
  50. On Ramsey graphs. (in Russian) (with Khadzhiivanov, N.) God. Sofij. Univ., Fak. Mat. Mech. 78 (1984), 211-214.
  51. Zykov numbers and some of their applications in Ramsey theory. (in Russian) Serdica 9 (1983), 161-167.
  52. The minimum number of 4-anticliques of some graphs without triangles. (Russian) (with Khadzhiivanov, N.) Annuaire Univ. Sofia Fac. Math. Mech. 77 (1983), 163-174.
  53. The minimal number of 5-anticliques in 14-vertex graphs without triangles. (in Russian) (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 36 (1983), 1155-1157.
  54. On the number of 5-anticliques in graphs which have 14 vertices and less than one 3-clique. (in Russian) (with Khadzhiivanov, N.) Mathematics and education in mathematics, Proc. 12th Spring Conf. Union Bulg. Math., Sunny Beach, 1983, 129-132 (1983).
  55. On the generalized Turan's theorem and on an extension of this theorem. (in Russian) (with Khadzhiivanov, N.) God. Sofij. Univ., Fak. Mat. Mekh. 77 (1983), n. 1, 231-242 (1988).
  56. On extremal 2-colorings of the edges of the complete graph with thirteen vertices. (with Khadzhiivanov, N., Pashov I.) Godishnik Vissh, Ped. Inst. Shuman - Mat. Fak. vol. 7B (1983), 53-64.
  57. An example of the 16-vertex Ramsey (3, 3)-graph with clique number 4. (in Russian) (with Khadzhiivanov, N.) Serdica 9 (1983), 74-78.
  58. Uniqueness of a 13-vertex graph with independence number 4 and with one triangle. (in Russian) (with Khadzhiivanov, N., Pashov, I.) C. R. Acad. Bulg. Sci. 35 (1982), 1363-1366.
  59. The number of monochromatic p-cliques in two-colorings of the edges of certain complete graphs. (in Russian) (with Pashov, I., Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 35 (1982), 439-442.
  60. The number of discrete 4-vertex subgraphs of a graph without triangles. (in Russian) (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 35 (1982), 909-912.
  61. On proper 3-coloring of the edges of complete graphs. (in Bulgarian) Mathematics and education in mathematics, Proc. 11th Spring Conf. Union Bulg. Math., Sunny Beach, 1982, 242-247 (1982).
  62. Description of the graphs with 13 vertices having a unique triangle and a unique 5-anticlique. (in Russian) (with Khadzhiivanov, N.) God. Sofij. Univ., Fak. Mat. Mekh. 76 (1982), 91-107 (1987).
  63. Sharpening of Lin's inequalities relating to Ramsey theory (in Russian) C. R. Acad. Bulg. Sci. 34 (1981), 307-310.
  64. On a certain constant connected with Ramsey (3, 4)-graphs. (in Russian) Serdica 7 (1981), 366-371.
  65. Lower bound for some constants related to Ramsey graphs. (in Russian) Annuaire Univ. Sofia Fac. Math. Mech. 75 (1981), 27-38.
  66. Generalization of a certain theorem of Greenwood and Gleason on three-colorings of the edges of a complete graph with 17 vertices. (in Russian) C. R. Acad. Bulg. Sci. 34 (1981), 1209-1212.
  67. Extremal problems for graphs with filters. (in Russian) (with Khadzhiivanov, N.) PLISKA, Stud. Math. Bulg. 2 (1981), 119-123.
  68. Certain remarks on Ramsey multiplicities. (in Russian) Mathematics and education in mathematics, Proc. 10th Spring Conf. Union Bulg. Math., Sunny Beach, 1981, 176-179 (1981).
  69. An extremal property of the Petersen graph (in Russian) (with Khadzhiivanov, N.) Annuaire Univ. Sofia Fac. Math. Mech. 75 (1981), 115-123.
  70. An example of a 15-vertex Ramsey (3, 3)-graph with the clique number 4. (in Russian) C. R. Acad. Bulg. Sci. 34 (1981), 1487-1459.
  71. Some applications of Zykov's numbers in Ramsey's theory. (in Russian; English summary) God. Sofij. Univ., Fak. Mat. Mekh. 74 (1980), 29-50 (1986).
  72. Ramsey graphs and some constants related to them. (in Bulgarian) Ph. D. Thesis, University of Sofia, Sofia, 1980.
  73. On the independence number of minimal t-graphs. (in Russian) Mathematics and education in mathematics, Proc. 9th Spring Conf. Union Bulg. Math., Sunny Beach, 1980, 74-78 (1980).
  74. On the existence of a minimal t-graph with a given number of vertices. (in Russian) Serdica 6 (1980), 270-274.
  75. On minimal t-graphs. (in Russian) (with Khadzhiivanov, N.) Serdica 6 (1980), 128-142.
  76. On an assumption of Lin about Ramsey-Graham-Spencer numbers. (in Russian) C. R. Acad. Bulg. Sci. 33 (1980), n. 9, 1171-1174.
  77. A new estimation from below for the Graham-Spencer number N(3, 5). (in Russian) Serdica 6 (1980), 373-383.
  78. Up to isomorphism there exists only one minimal t-graph with nine vertices. (in Russian) God. Sofij. Univ., Fak. Mat. Mekh. 73 (1979), 169-184 (1986).
  79. On the number of nontrivial solutions of Fermat's equation xn + yn = zn in a Galois field. (in Russian) (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 32 (1979), 557-560.
  80. On the Ramsey (3, 4)-graphs. (in Russian) God. Sofij. Univ., Fak. Mat. Mekh. 73 (1979), 185-190 (1986).
  81. On the Graham-Spencer number (in Russian) (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 32 (1979), 155-158.
  82. On edgewise 2-colored graphs containing a monochromatic triangle. (in Russian) (with Khadzhiivanov, N.) Serdica, 303-305.
  83. t-graphs with clique number 4. (in Russian) (with Khadzhiivanov, N.) Mathematics and education in mathematics, Proc. 8th Spring Conf. Union Bulg. Math., Sunny Beach, 1979, 565-577 (1979).
  84. Sharpening of a theorem of Greenwood and Gleason on the colorings of the edges of a complete graph with nine vertices. (in Russian) (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 31 (1978), 631-633.
  85. On the existence of a minimal t-graph with nine vertices. (in Russian) Annuaire Univ. Sofia Fac. Math. Mech. 72 (1978), 271-276.
  86. The number of p-cliques in graphs with p-filters. (in Russian) (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 30 (1977), 1231-1234.
  87. On the maximum of the numbers of cliques in some graphs (with Khadzhiivanov, N.) Mathematics and education in mathematics, Proc. 6th Spring Conf. Union Bulg. Math., Sunny Beach, 1977, 131-134.
  88. Inequalities connected with graphs. (in Russian) (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 30 (1977), 635-638.
  89. Extremal problems for s-graphs and a theorem of Turan. (in Russian) (with Khadzhiivanov, N.) Serdica 3 (1977), 117-125.
  90. p-sequences of graphs and extremal properties of Turan graphs. (in Russian) (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 30 (1977), 635-638.
  91. On the maximum number of edges of a graph. (in Russian) (with Khadzhiivanov, N.) C. R. Acad. Bulg. Sci. 29 (1976), 1575-1578.
  92. On some colorings in two colors of the edges of the complete graph with nine vertices. (in Russian) (with Khadzhiivanov, N.) God. Sofij. Univ., Fak. Mat. Mekh. 71 (1976/1977), Part II, 92-115 (1986).
  93. Maximum of the number of cliques of some graphs. (in Russian) (with Khadzhiivanov, N.) God. Sofij. Univ., Fak. Mat. Mekh. 70 (1975), 23-26.
  94. A new proof of a theorem about the maximum number of p-cliques of graphs. (in Russian) (with Khadzhiivanov, N.) Annuaire Univ. Sofia Fac. Math. Mech. 70 (1975), 93-98.
  95. On the representation of the abstract wreath product of groups by permutations. (in Russian) God. Sofij. Univ., Fak. Mat. Mekh. (1972/1973), 565-572 (1976).
  96. On the multiply-transitive groups. (in Russian) God. Sofij. Univ., Fak. Mat. Mekh. 65 (1970/1971), 219-224 (1972).
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