Book:

cover       Svante Janson, Tomasz Luczak and Andrzej Rucinski,
Random Graphs , Wiley, New York, 2000, 333+xi pp.
ISBN 0-471-17541-2
(see also errata)

Papers:

  1. On matchings and hamiltonian cycles in subgraphs of random graphs, Annals of Discrete Math. 33 (1987) 171-185.
  2. On k-leaf connectivity of a random graph, J.Graph Theory 12 (1988) 1-10.
  3. The automorphisms group of random graphs with given number of edges, Math. Proc. Camb. Phil. Soc. 104 (1988) 441-449.
  4. Critical probability bounds for two-dimensional site percolation models, J.Physics A 21 (1988) 3131-3138 (with John C.Wierman).
  5. Maximal induced trees in sparse random graphs, Discrete Math. 72 (1988) 257-265 (with Zbigniew Palka).
  6. The chromatic number of random graphs at the double jump threshold, Combinatorica 9 (1989) 39-49 (with John C.Wierman).
  7. Counterexamples in AB percolation, J.Physics A 22 (1989) 185-191 (with John C.Wierman).
  8. On the number of sparse connected graphs, Random Structures & Algorithms 1 (1990) 171-174.
  9. Hamiltonian cycles in a class of random graphs: one step further, Proceedings of Random Graphs'87, (Michal Karonski, Jerzy Jaworski, Andrzej Rucinski, eds.), Wiley, Chichester 1990, 53-63 (with Alan M.Frieze).
  10. An exponential bound for the probability of nonexistence of a specified subgraph in a random graph, Proceedings of Random Graphs'87, (Michal Karonski, Jerzy Jaworski, Andrzej Rucinski, eds.), Wiley, Chichester 1990, 73-88 (with Svante Janson and Andrzej Rucinski).
  11. On the equivalence of two basic models of random graphs, Proceedings of Random Graphs'87, (Michal Karonski, Jerzy Jaworski, Andrzej Rucinski, eds.), Wiley, Chichester 1990, 151-158.
  12. Components behavior near the critical point of the random graph process, Random Structures & Algorithms 1 (1990) 287-310.
  13. The phase transition in the evolution of random digraphs, J.Graph Theory 14 (1990) 217-223.
  14. Edge disjoint spanning trees in random graphs, Periodica Math. Hung. 21 (1990) 35-37 (with Alan M.Frieze).
  15. Stochastic structure and nonlinear dynamics of food webs: qualitative stability in a Lotka-Volterra cascade model, Proceedings of the Royal Society (London) ser B 240(1990) 607-627 (with Joel E.Cohen, Charles M.Newman and Zhi Ming Zhou).
  16. Holes in random graphs, Discrete Appl.Math. 30 (1991) 213-219.
  17. Tree-matchings in graph processes, SIAM J.Discrete Math. 4 (1991) 107-120 (with Andrzej Rucinski).
  18. The chromatic number of random graphs, Combinatorica 11 (1991) 45-54.
  19. A note on the sharp concentration of the chromatic number of random graphs, Combinatorica 11 (1991) 295-297.
  20. Size and connectivity of the k-core of a random graph, Discrete Math. 91 (1991) 61-68.
  21. Stability of vertices in random Boolean cellular automata, Random Structures & Algorithms 2 (1991) 327-334 (with Joel E.Cohen).
  22. How to deal with unlabelled random graphs, J.Graph Theory 15 (1991) 303-316.
  23. Cycles in a random graph near the critical point, Random Structures & Algorithms 2 (1991) 421-440.
  24. When does the zero-one law hold? J.Amer.Math.Soc. 4 (1991) 451-468 (with Joel H. Spencer).
  25. On random subsets of projective spaces, Colloq.Math. LXII (1991) 353-356 (with Wojciech Kordecki).
  26. Cycles in random graphs, Discrete Math. 98 (1991) 231-236.
  27. First order properties of random posets, Order 8 (1991) 291-297.
  28. On the independence and chromatic numbers of random regular graphs, J.Combin.Th.Ser.B 54 (1992) 123-132 (with Alan M.Frieze).
  29. Trophic levels in community food webs, Evolutionary Ecology 6 (1992) 73-89 (with Joel E.Cohen).
  30. The evolution of random subgraphs of the cube, Random Structures & Algorithms 3 (1992) 55-90 (with Béla Bollobás, Yoshiharu Kohayakawa ).
  31. Subgraphs of large minimal degree, Random Graphs, vol. 2, (Alan M.Frieze, Tomasz Luczak, eds.), Wiley, New York (1992) 59-68 (with Paul Erdös and Joel H. Spencer).
  32. Sparse random graphs with a given degree sequence, Random Graphs, vol. 2, (Alan M.Frieze, Tomasz Luczak, eds.), Wiley, New York (1992) 165-182.
  33. Balanced extensions of sparse graphs, Proc. of IV Czechoslovak Symposium on Combinatorics, Graphs and Complexity, Prachatice, 1990 (Jaroslav Nesetril and Miroslav Fiedler, eds.), Annals of Discrete Math. 51 (1992) 191-203 (with Andrzej Rucinski).
  34. Components of random forests, Combinatorics, Probability & Computing 1 (1992) 35-52 (with Boris G.Pittel).
  35. Convex hulls of dense balanced graphs, J. Comput. Appl. Math. 41 (1992) 205-213 (with Andrzej Rucinski).
  36. Ramsey properties of random graphs, J.Combin.Th.Ser.B 56 (1992) 55-68 (with Bernd Voigt and Andrzej Rucinski).
  37. Giant components in three-parameter random directed graphs, Advances in Appl.Probab. 24 (1992) 845-857 (with Joel E.Cohen).
  38. Cycles in a uniform graph process, Combinatorics, Probability & Computing 1 (1992) 223-239 (with Jerzy Jaworski).
  39. The size of the largest hole in a random graph, Discrete Math. 112 (1993) 151-163.
  40. The birth of the giant component, Random Structures & Algorithms 3 (1993) 233-358 (with Svante Janson, Donald E.Knuth and Boris G.Pittel).
  41. Stratigraphy of a random acyclic directed graph: the size of trophic levels in the cascade model, Annals of Appl. Probab. 3 (1993) 403-420 (with Joel E.Cohen).
  42. Approximations with axis-aligned rectangles,  Lecture Notes in Computer Science 710 (1993) 244-255 (with Paul Fischer, Klaus-Uwe Höffgen and Hanno Lefmann).
  43. Changes of leadership in a random graph process, Random Structures & Algorithms 5 (1994) 243-252 (with Paul Erdös).
  44. The structure of a random graph near the point of the phase transition, Tran.Amer.Math. Soc. 341 (1994) 721-748 (with Boris G.Pittel and John C.Wierman).
  45. On random generation of the symmetric group, Combinatorics, Probability & Computing 2 (1993) 505-512 (with László Pyber).
  46. On Ramsey minimal graphs, Electronic J.Comb. 1 (1994) paper no.4.
  47. On the clique number of a random overlap graph, J.Appl.Probab. 31 (1994) 582-588 (with Zbigniew Palka)
  48. On the evolution of random Boolean functions, Extremal Problems for Finite Sets, Visegrád 1991 (Hungary), (Peter Frankl, Zoltan Füredi, Gyula O.H. Katona, Dezsö Miklós, eds.), Bolyai Society Mathematical Studies 3 (1994) 137-156 (with Béla Bollobás, Yoshiharu Kohayakawa).
  49. On the k-diameter of k-regular k-connected graphs, Discrete Math. 133 (1994) 291-296 (with D.Frank Hsu).
  50. On the diameter and radius of random subgraphs of the cube, Random Structures & Algorithms 5 (1994) 627-648 (with Béla Bollobás and Yoshiharu Kohayakawa).
  51. Independent transversal in sparse partite hypergraphs, Combinatorics, Probability & Computing 3 (1994) 293-296 (with Paul Erdös and András Gyárfás).
  52. Phase transition phenomena in random discrete structures, Recent Trends in Discrete Mathematics (Walter Deuber, Hans-Jürgen Prömel, Bernd Voigt, eds.), Discrete Math. 136 (1994) 225-242.
  53. Sparse anti-Ramsey graphs, J.Combin.Th.Ser.B 63 (1995) 146-152 (with Yoshiharu Kohayakawa ).
  54. Connectivity properties of random subgraphs of the cube, Random Structures & Algorithms 6 (1995) 221-230 (with Béla Bollobás and Yoshiharu Kohayakawa).
  55. A note on the density of sum-free-sets, J.Combin.Th.Ser.A 70 (1995) 334-336.
  56. Convergence in homogeneous random graphs, Random Structures & Algorithms 6 (1995) 371-392 (with Saharon Shelah).
  57. The number of trees with a large diameter, J.Austral. Math.Soc. Ser A 58 (1995) 298-311.
  58. Turán's extremal problem in random graphs: forbidding even cycles, J.Combin.Th. Ser.B 64 (1995) 273-287 (with Penny E. Haxell and Yoshiharu Kohayakawa ).
  59. The induced size-Ramsey number of cycles, Combinatorics, Probability & Computing 4 (1995) 217-239 (with Penny E. Haxell and Yoshiharu Kohayakawa )
  60. On sum-free sets of natural numbers, Resenhas IME-USP 2 (1995) 229-238.
  61. A note on triangle-free graphs, Random Discrete Structures, (David Aldous and Robin Pemantle, eds.), IMA Volumes in Mathematics and its Applications, vol.76, Springer Verlag, 1995, 117-120. (with Paul Erdös, Svante Janson and Joel H. Spencer)
  62. On the evolution of a random tournament, Discrete Math. 148 (1996) 311-316 (with Andrzej Rucinski, Jacek Gruszka).
  63. On induced Ramsey numbers for graphs with bounded maximum degree, J.Combin.Th. Ser.B 66 (1996) 324-333 (with Vojtech Rödl).
  64. Arithmetic progressions of length three in subsets of a random set, Acta Arithmetica LXXV (1996) 133-163 (with Yoshiharu Kohayakawa and Vojtech Rödl).
  65. Turán's extremal problem in random graphs: forbidding odd cycles, Combinatorica 16 (1996) 107-122 (with Penny E. Haxell and Yoshiharu Kohayakawa ).
  66. Random hypergraphs, Combinatorics, Paul Erdös is Eighty, vol.2 (Dezsö Miklós, Vera T.Sós, Tamás Szõnyi, eds.), Budapest, 1996, Bolyai Society Mathematical Studies 2, 283-293 (with Michal Karonski).
  67. The phase transition in a random graph, Combinatorics, Paul Erdös is Eighty, vol.2 (Dezsö Miklós, Vera T.Sós, Tamás Szõnyi, eds.), Budapest, 1996, Bolyai Society Mathematical Studies 2, 399-422.
  68. Ramsey-type results for oriented trees, J.Graph Theory 22 (1996) 1-8 (with Yoshiharu Kohayakawa and Vojtech Rödl).
  69. On strongly sum-free subsets of abelian groups, Colloq.Math. LXXI (1996) 149-151 (with Tomasz Schoen).
  70. Graphs in which each C4 spans K4, Discrete Math. 154 (1996) 263-268 (with Paul Erdös and András Gyárfás).
  71. Large subgraphs of minimal density or degree, J.Combin.Math. and Combin.Computing 22 (1996) 87-96 (with Paul Erdös, Ralph Faudree and Arun Jagota).
  72. A note on restricted vertex Ramsey numbers, Periodica Math. Hung. 33 (1996) 101-104 (with Sebastian Urbanski).
  73. Graphs without small odd cycles are nearly bipartite, Discrete Math. 163 (1997) 279-284 (with Ervin Györi and Alexandr V. Kostochka).
  74. Dense difference sets and their combinatorial structure, Mathematics of Paul Erdös, Proceedings of Prague Conference, Springer-Verlag, 1997, 165-175 (with Vitaly Bergelson, Paul Erdös, Neil Hindman).
  75. On the fractional dimension of sets of continued fractions, Mathematika 44 (1997) 50-53.
  76. The number of sparsely edges connected uniform hypergraphs, Discrete Math. 171 (1997) 153-168 (with Michal Karonski).
  77. On K4-free subgraphs of random graphs, Combinatorica 17 (1997) 173-213 (with Yoshiharu Kohayakawa and Vojtech Rödl).
  78. A suboptimal lossy data compression based on an approximate pattern matchings, IEEE Transactions on Information Theory 43 (1997) 1439-1451 (with Wojciech Szpankowski).
  79. Convergence of probabilities for the second order monadic properties of a random mapping, Random Structures & Algorithms 11 (1997) 277-295 (with Lubos Thoma).
  80. On infinite sum-free sets of natural numbers, J.Number Theory 66 (1997) 211-224 (with Tomasz Schoen).
  81. On a parallel randomized algorithm for finding a maximal independent set in a linear hypergraph, J.Algorithms 25 (1997) 311-320 (with Edyta Szymanska).
  82. Independent finite sums in graphs defined on the natural numbers, Discrete Math. 181 (1998) 289-294 (with Vojtech Rödl and Tomasz Schoen).
  83. Endomorphisms of partially ordered sets, Combinatorics, Probability & Computing 7 (1998) 33-46 (with Dwight Duffus, Vojtech Rödl and Andrzej Rucinski).
  84. A greedy algorithm for estimating the height of random trees, SIAM J.Discrete Math. 11 (1998) 318-329.
  85. Small bases for finite groups, Colloq.Math. LXXVIII (1998) 35-37 (with Tomasz Schoen).
  86. Biased positional games on hypergraphs, Studia Scientarum Matematicarum Hung. 34 (1998) 141-149 (with Dwight Duffus and Vojtech Rödl).
  87. Random trees and random graphs, Random Structures & Algorithms 13 (1998) 485-500.
  88. Partitioning two-coloured complete graphs into monochromatic cycles, Combinatorics, Probability & Computing 7 (1998) 423-436 (with Vojtech Rödl and Endre Szemerédi).
  89. On the connectivity of random subsets of projective spaces, Discrete Math. 196 (1999) 207-217 (with Wojciech Kordecki).
  90. R(Cn,Cn,Cn) < (4+o(1))n, J.Combin.Th.Ser.B 75 (1999) 174-187.
  91. On the minimum number of edges giving maximum oriented chromatic number. In Contemporary Trends in Discrete Mathematics (Ronald L. Graham, Jan Kratochvil, Jaroslav Nesetril, Fred S. Roberts, eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 49, AMS, 1999, 179-182 (with Alexandr V. Kostochka, Gábor Simonyi and Eric Sopena).
  92. A note on the maximum automorphism group of self-complementary graphs, Mathematica Slovaka 50 (2000) 17-24.
  93. Embedding trees into graphs of large girth, Discrete Math. 216 (2000) 273-278 (with Penny E. Haxell).
  94. On triangle-free random graphs, Random Structures & Algorithms 16 (2000) 260-276.
  95. On the maximal density of sum-free sets, Acta Arithmetica XCV (2000) 225-229 (with Tomasz Schoen).
  96. Biased positional games for which random strategies are nearly optimal, Combinatorica 20 (2000) 477-488 (with Malgorzata Bednarska).
  97. Biased positional games and the phase transition, Random Structures & Algorithms 18 (2001) 141-152 (with Malgorzata Bednarska).
  98. On the number of maximal sum-free sets, Proc.Amer.Math.Soc. 129 (2001) 2205-2207 (with Tomasz Schoen).
  99. On minimal vertex Folkman graphs, Discrete Math. 236 (2001) 245-262 (with Andrzej Rucinski and Sebastian Urbanski).
  100. Sum-free subsets of right cancellative semigroups, European J. Combin. 22 (2001) 999-1002 (with Tomasz Schoen).
  101. Sum-free sets in abelian groups, Israel J. Math. 125 (2001) 347-367 (with Vsevolod F. Lev and Tomasz Schoen).
  102. Vertex Ramsey properties of families of graphs, J.Combin.Th. Ser.B 84 (2002) 240-248 (with Andrzej Rucinski and Sebastian Urbanski).
  103. The phase transition in a random hypergraph, J. Comput. Appl. Math. 142 (2002) 125-135 (with Michal Karonski).
  104. On induced Ramsey numbers, Discrete Math. 251 (2002) 87-96 (with Izolda Gorgol).
  105. Ramsey numbers for trees of small maximum degree, Combinatorica 22 (2002) 287-320 (with Penny E. Haxell and Peter W. Tingley).
  106. On the discrepancy of combinatorial rectangles, Random Structures & Algorithms 21 (2002) 205-215 (with Noga Alon, Benjamin Doerr, and Tomasz Schoen).
  107. Ramsey properties of families of graphs, J.Combin.Th. Ser.B 86 (2002) 413-419 (with Ronald Graham, Vojtech Rödl and Andrzej Rucinski).
  108. Solution-free sets for linear equations, J.Number Theory 102 (2003) 11-22 (with Tomasz Schoen).
  109. Quantum walks on cycles, Physics Letters A 317 (2003) 21-25 (with Malgorzata Bednarska, Andrzej Grudka, Pawel Kurzynski, and Antoni Wójcik).
  110. Edge weights and vertex colours, J.Combin.Th. Ser.B 91 (2004) 151-157 (with Michal Karonski and Andrew G. Thomason).
  111. A note on projective graphs, J.Graph Theory 47 (2004) 81-86 (with Jaroslav Nešetřil).
  112. Claw-free 3-connected P11-free graphs are hamiltonian, J.Graph Theory 47 (2004) 111-121 (with Florian Pfender).
  113. Pancyclicity of 3-connected graphs:pairs of forbidden subgraphs, J.Graph Theory 47 (2004) 183-202 (with Ronald J. Gould and Florian Pfender).
  114. A note on unique representation bases for the integers, Funct. Approx. Comment. Math. 32 (2004) 67-70 (with Tomasz Schoen).
  115. Quasiperiodic dynamics of a quantum walk on the line, Phys. Rev. Letters 93 (2004) 180601 (with Malgorzata Bednarska, Andrzej Grudka, Pawel Kurzyñski, and Antoni Wójcik).
  116. Examples of nonuniform limiting distributions for the quantum walks on even cycles, International Journal of Quantum Information 2 (2004) 453-460 (with Malgorzata Bednarska, Andrzej Grudka, Pawel Kurzyñski, and Antoni Wójcik).
  117. Torpid mixing of the Wang-Swendsen-Kotecký algorithm for sampling colorings, J.Discrete Algorithms 3 (2005) 92-100 (with Eric Vigoda).
  118. Mobile mixing, Lecture Notes in Computer Science 3506 (2005), 380-393 (with Marcin Gogolewski and Miroslaw Kutylowski).
  119. Phase transition phenomena in random discrete structures. Proceedings of the 4th European Congress of Mathematics, Stockholm, 2004 (A. Laptev, ed.), European Math. Soc., Zurich (2005) 257-268.
  120. Unmodulated spin chains as universal quantum wires, Phys. Review A 72 (2005) 034303 (with Malgorzata Bednarska, Tomasz Gdala, Andrzej Grudka, Pawel Kurzyñski, and Antoni Wójcik).
  121. The Ramsey number for hypergraph cycles I, J.Combin.Th.Ser.A 113 (2006) 67-83 (with Penny E. Haxell, Yuejian Peng, Vojtech Rödl, Andrzej Ruciñski, Miklós Simonovits, Jozef Skokan).
  122. The phase transition in the cluster-scaled model of a random graph, Random Structures & Algorithms 28 (2006) 215-246 (with Malwina J. Luczak).
  123. Constructive upper bounds for cycle-saturated graphs of minimum size, Electronic J.Comb. 13 (2006) #R29, 1-19. (with Ronald J. Gould and John R. Schmitt).
  124. The connectivity threshold for the min-degree random graph, Random Structures & Algorithms 29 (2006) 105-120 (with Mihyun Kang, Youngmee Koh, and Sangwook Ree).
  125. When is a random graph projective?, European J. Combin. 27 (2006) 1147-1154 (with Jaroslav Nešetřil).
  126. On the structure of triangle-free graphs of large minimum degree, Combinatorica 26 (2006) 489-493.
  127. Regularity and randomness, Proceedings of the International Congress of Mathematicians, Madrid, 22-30 August 2006, (Marta Sanz-Solé, Javier Soria, Juan Luis Varona, Joan Verdera, eds.), EMS Publishing House, 2006, 899-910.
  128. Protean graphs, Internet Mathematics 3 (2006) 21-40 (with Pawe³ Pra³at).
  129. A probabilistic approach to the dychotomy problem, SIAM J.Computing 36 (2006) 835-843 (with Jaroslav Nesetril).