The probability that a random multigraph is simple

Combinatorics Probability and Computing

Volumn 18, Issue 1-2, 2009, Pages 205-225

  Janson, Svante ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC FORMULA; CONFIGURATION MODEL; MAXIMUM DEGREE; MULTIGRAPH; MULTIGRAPHS; VERTEX DEGREE;

ASYMPTOTIC ANALYSIS;

PROBABILITY;

EID: 64249139214     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548308009644     Document Type: Article

References (15)

1. Bender, E. A. and Canfleld, E. R. (1978) The asymptotic number of labeled graphs with given degree sequences. J. Combin. Theory Ser. A 24 296-307.
2. Bollobás, B. (1980) A probabilistic proof of an asymptotic formula for the number of labelled regular graphs. Europ. J. Combin. 1 311-316.
3. Bollobás, B. (2001) Random Graphs, 2nd edn, Cambridge University Press, Cambridge.
4. Cooper, C. (2004) The cores of random hypergraphs with a given degree sequence. Random Struct. Alg. 25 353-375.
5. Cooper, C. and Frieze, A. (2004) The size of the largest strongly connected component of a random digraph with a given degree sequence. Combin. Probab. Comput. 13 319-337.
6. Gut, A. (2005) Probability: A Graduate Course, Springer, New York.
7. Janson, S. and Luczak, M. (2007) A simple solution to the κ-core problem. Random Struct. Alg. 30 50-62.
8. Janson, S., Łuczak, T. and Ruciński, A. (2000) Random Graphs, Wiley, New York.
9. McKay, B. D. (1984) Asymptotics for 0-1 matrices with prescribed line sums. In Enumeration and Design (Waterloo, Ont., 1982), Academic Press, Toronto, ON, pp. 225-238.
10. McKay, B. D. (1985) Asymptotics for symmetric 0-1 matrices with prescribed row sums. Ars Combin. 19A 15-25.
11. McKay, B. D. and Wormald, N. C. (1990) Uniform generation of random regular graphs of moderate degree. J. Algorithms 11 52-67.
12. McKay, B. D. and Wormald, N. C. (1990) Asymptotic enumeration by degree sequence of graphs of high degree. Europ. J. Combin. 11 565-580.
13. 1/2). Combinatorica 11 369-382.
14. Wormald, N. C. (1978) Some problems in the enumeration of labelled graphs. PhD thesis, University of Newcastle.
15. Wormald, N. C. (1981) The asymptotic distribution of short cycles in random regular graphs. J. Combin. Theory Ser. B 31 168-182.