How likely is an I.I.D. Degree sequence to be graphical?

Annals of Applied Probability

Volumn 15, Issue 1 B, 2005, Pages 652-670

  Arratia, Richard ^a   Liggett, Thomas M ^b  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Degree sequences; Extremes of i.i.d. Random variables; Random graphs; Simple graphs

Indexed keywords

EID: 14544299288     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/105051604000000693     Document Type: Article

References (16)

1. AIELLO, W., CHUNG, F. and Lu, L. (2001). A random graph model for power law graphs. Experiment. Math. 10 53-66.
2. ALBERT, R. and BARABÁSI, A. (2002). Statistical mechanics of complex networks. Rev. Modern Phys. 74 47-97.
3. BOLLOBÁS, B. (2001). Random Graphs, 2nd ed. Cambridge Univ. Press.
4. BOLLOBÁS, B. and RIORDAN, O. (2003). Mathematical results on scale-free random graphs. In Handbook of Graphs and Networks: From the Genome to the Internet (S. Bornholdt and H. G. Schuster, eds.) 1-34. Wiley-VCH, New York.
5. CHOUDUM, S. A. (1986). A simple proof of the Erdos-Gallai theorem on graph sequences. Bull. Austral. Math. Soc. 33 67-70.
6. DURRETT, R. (1996). Probability: Theory and Examples, 2nd ed. Duxbury, N. Scituate, MA.
7. EPSTEIN, B. and SOBEL, M. (1953). Life testing. J. Amer. Statist. Assoc. 48 486-502.
8. ERDOS, P. and GALLAI, T. (1960). Graphs with given degree of vertices. Mat. Lapok 11 264-274.
9. JANSON, S., LUCZAK, T. and RUCINSKI, A. (2000). Random Graphs. Wiley, New York.
10. JERRUM, M., MCKAY, B. and SINCLAIR, A. (1992). When is a graphical sequence stable? In Random Graphs (A. Frieze and T. Luczak, eds.) 2 101-115. Wiley, New York.
11. JERRUM, M. and SINCLAIR, A. (1990). Fast uniform generation of regular graphs. Theoret. Comput. Sci. 7391-100.
12. LEADBETTER, M. R., LINDGREN, G. and ROOTZÉN, H. (1983). Extremes and Related Properties of Random Sequences and Processes. Springer, New York.
13. PITTEL, B. (1999). Confirming two conjectures about the integer partitions. J. Combin. Theory Ser. A 88 123-135.
14. RÉNYI, A. (1953). On the theory of ordered samples. Acta Math. Acad. Sci. Hungar. 4 191-231.
15. SIERKSMA, G. and HOOGEVEEN, H. (1991). Seven criteria for integer sequences being graphic. J. Graph Theory 15 223-231.
16. STEGER, A. and WORMALD, N. (1999). Generating random graphs quickly. Combin. Probab. Comput. 8 377-396.