For which densities are random triangle-free graphs almost surely bipartite?

Combinatorica

Volumn 23, Issue 1, 2003, Pages 105-150

  Osthus, Deryk ^a   Prömel, Hans Jürgen ^a   Taraz, Anusch ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038720025     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00493-003-0016-1     Document Type: Article

References (20)

1. M. BEHRISCH: Random graphs with a forbidden short cycle, Diploma thesis, Institut für Informatik, Humboldt-Universität zu Berlin, 2002.
2. B. BOLLOBÁS: Random Graphs, Academic Press, London, 1985.
3. P. ERDOS, S. JANSON, T. ŁUCZAK and J.H. SPENCER: A note on triangle-free graphs, in Random discrete structures, eds. D. Aldous and R. Pemantle, IMA Vol. 76, Springer, New York (1995), 117-120.
4. nfree graphs, in International Colloquium on Combinatorial theory, Atti dei Convegni Lincei 17, Vol. 2, Rome, 19-27, 1976.
5. P. ERDOS and A. RÉNYI: On the evolution of random graphs, Magyar Tud. Akad. Mat. Kut. Int. Közl. 5 (1960), 17-61.
6. 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, eds. M. Karoński, J. Jaworski and A. Ruciński, John Wiley & Sons (1987), 73-87.
7. S. JANSON, T. ŁUCZAK and A. RUCIŃSKI: Random Graphs, Wiley-Interscience, New York, 2000.
8. 2/log t, Random Struct. Algorithms 7 (1995), 173-207.
9. Y. KOHAYAKAWA and B. KREUTER: Threshold functions for asymmetric Ramsey properties involving cycles, Random Struct. Algorithms 11 (1997), 245-276.
10. Y. KOHAYAKAWA, T. ŁUCZAK and V. RÖDL: Arithmetic progressions of length three in subsets of a random set, Acta Arithmetica LXXV (1996), 133-163.
11. E. LAMKEN and B.L. ROTHSCHILD: The numbers of odd-cycle-free graphs, in Finite and infinite sets, eds. A. Hajnal, L. Lovász, and V.T. Sós, Colloq. Math. Soc. János Bolyai 37, North-Holland, Amsterdam (1984), 547-553.
12. T. ŁUCZAK: On triangle-free random graphs, Random Struct. Algorithms 16 (2000), 260-276.
13. D. OSTHUS: On the Evolution of Random Discrete Structures, Ph.D. Dissertation, Institut für Informatik, Humboldt-Universität zu Berlin, 2000.
14. D. OSTHUS, H.J. PRÖMEL and A. TARAZ: Almost all graphs with high girth and suitable density have high chromatic number, Journal of Graph Theory 37 (2001), 220-226.
15. H.J. PRÖMEL and A. STEGER: Random l-colourable graphs, Random Struct. Algorithms 6 (1995), 21-37.
16. H.J. PRÖMEL and A. STEGER: On the asymptotic structure of sparse triangle free graphs, Journal of Graph Theory 21 (1996), 137-151.
17. H.J. PRÖMEL and A. STEGER: Counting H-free graphs, Discr. Math. 154 (1996), 311-315.
18. J.H. SPENCER: Threshold functions for extension statements, J. Combin. Theory Ser. A 53 (1990), 286-305.
19. A. STEGER: unpublished manuscript, Technische Universität München, 1999.
20. N.C. WORMALD: The perturbation method and triangle-free random graphs, Random Struct. Algorithms 9 (1996), 253-270.