The perturbation method and triangle-free random graphs

Random Structures and Algorithms

Volumn 9, Issue 1, 1996, Pages 253-270

  Wormald, Nicholas C ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444445002     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1098-2418(199608/09)9:1/2<253::aid-rsa15>3.0.co;2-o     Document Type: Article

References (13)

1. P. Erdos and A. Rényi, On the evolution of random graphs, Publ. Math. Inst. Hung. Acad. Sci., 5, 17-61 (1960).
2. A. Frieze, On small subgraphs of random graphs, in Random Graphs Vol. 2, A. Frieze and T. Łuczak, Eds., Wiley, New York, 1992, pp. 67-90.
3. C. D. Godsil and B. D. McKay, Asymptotic enumeration of Latin rectangles, J. Combinat. Theor. Ser. B, 48, 19-44 (1990).
4. S. Janson, T. Łuczak, and A. Ruciński, An exponential bound for the probability of nonexistence of a specified subgraph in a random graph, in Random Graphs '87, M. Karonski, J. Jaworski, and A. Rucirńki, Eds., Wiley, New York, 1990, pp. 73-87.
5. B. D. McKay, Subgraphs of random graphs with specified degrees, Cong. Numer., 33, 213-223 (1981).
6. B. D. McKay, Asymptotics for symmetric 0-1 matrices with prescribed row sums, Ars Combinat., 19A, 15-25 (1985).
7. B. D. McKay and N. C. Wormald, Uniform generation of random regular graphs of moderate degree, J. Alg., 11, 52-67 (1990).
8. 1/2), Combinatorica, 11, 369-382 (1991).
9. H. J. Prömel and A. Steger, On the asymptotic structure of sparse triangle free graphs, J. Graph Theor., to appear.
10. H. J. Prömel and A. Steger, Counting H-free graphs, Discrete Math., to appear.
11. C. Stein, Asymptotic evaluation of the number of Latin rectangles, J. Combinat. Theor. Ser. A, 25, 38-49 (1978).
12. C. Stein, Approximate Computation of Expectations, Lecture Notes 7, IMS, Hayward, CA 1988.
13. N. C. Wormald, The perturbation method for small subgraphs of random graphs, preprint.