Hamilton cycles in the union of random permutations

Random Structures and Algorithms

Volumn 18, Issue 1, 2001, Pages 83-94

  Frieze, Alan ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035529275     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/1098-2418(200101)18:1<83::AID-RSA6>3.0.CO;2-I     Document Type: Article

References (22)

1. E.A. Bender and E.R. Canfield, The asymptotic number of labelled graphs with given degree sequences, J Combin Theory, Ser A 24 (1978), 296-307.
2. B. Bollobás, Almost all regular graphs are Hamiltonian, Eur J Combin 4 (1983), 97-106.
3. B. Bollobás, A probabilistic proof of an asymptotic formula for the number of labelled regular graphs, Eur J Combin 1 (1980), 311-316.
4. A.Z. Broder and E. Shamir, On the second eigenvalue of random regular graphs, Proc Twenty-Eighth Annual IEEE Symp on the Foundations of Computer Science, 1987, pp. 286-294.
5. C. Cooper, The union of two random permutations does not have a directed Hamilton cycle, Random Struct Alg 18, 95-98.
6. C. Cooper and A.M. Frieze, Hamilton cycles in a class of random directed graphs, J Combin Theory Ser B 62 (1994), 151-163.
7. C. Cooper and A.M. Frieze, Hamilton cycles in random graphs and digraphs, Random Struct Alg 16 (2000), 369-401.
8. C. Cooper, A.M. Frieze, and M.J. Molloy, Hamilton cycles in random regular digraphs, Combin Probab Comput 3 (1994), 39-50.
9. T.I. Fenner and A.M. Frieze, Hamiltonian cycles in random regular graphs, J Combin Theory Ser B 37 (1984), 103-112.
10. J. Friedman, J. Kahn, and E. Szemerédi, On the second eigenvalue in random regular graphs, Proc Twenty-First Annual ACM Symp on Theory of Computing, 1989 pp. 587-598.
11. A.M. Frieze, Finding hamilton cycles in sparse random graphs, J Combin Theory Ser B 44 (1988), 230-250.
12. A.M. Frieze, R.M. Karp, and B. Reed, When is the assignment bound asymptotically tight for the asymmetric traveling-salesman problem?, SIAM J Comput 24 (1995), 484-493.
13. A.M. Frieze, M.R. Jerrum, M. Molloy, R. Robinson, and N.C. Wormald, Generating and counting Hamilton cycles in random regular graphs, J Alg 21 (1996), 176-198.
14. S. Janson, Random regular graphs: Asymptotic distributions and contiguity, Combin Probab Comput 4 (1995), 369-405.
15. B.D. Mckay, Asymptotics for symmetric 0-1 matrices with prescribed row sums, Ars Combinatoria 19A (1985), 15-25.
16. 1/2), Combinatorica 11 (1991), 369-382.
17. B.D. Mckay and N.C. Wormald, Asymptotic enumeration by degree sequence of graphs of high degree, Eur J Combin 11 (1990), 565-580.
18. M. Molloy, R.W. Robinson, H. Robalewska, and N.C. Wormald, 1-Factorisatons of random regular graphs, Random Struct Alg 10 (1997), 305-321.
19. R.C. Read, The enumeration of locally restricted graphs, J London Math Soc 35 (1980), 344-351.
20. R.W. Robinson and N.C. Wormald, Almost all cubic graphs are Hamiltonian, Random Struct Alg 3 (1992), 117-126.
21. R.W. Robinson and N.C. Wormald, Almost all regular graphs are Hamiltonian, Random Struct Alg 5 (1994), 363-374.
22. N.C. Wormald, Models of random regular graphs, Surveys in combinatorics, 1999 (J.D. Lamb and D.A. Preece (Editors)), Cambridge University Press, Cambridge, UK, 1999, pp. 239-298.