On Ramsey numbers of sparse graphs

Combinatorics Probability and Computing

Volumn 12, Issue 5-6 SPEC. ISS., 2003, Pages 627-641

  Kostochka, Alexandr ^a,b   Sudakov, Benny ^c,d  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

^c PRINCETON UNIVERSITY   (United States)

^d INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; NUMBER THEORY; PROBLEM SOLVING; THEOREM PROVING;

RAMSEY NUMBERS; SPARSE GRAPHS;

GRAPH THEORY;

EID: 2942571947     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0963548303005728     Document Type: Article

References (15)

1. Alon, N. (1994) Subdivided graphs have linear Ramsey numbers. J. Graph Theory 18 343-347.
2. Alon, N. and Spencer, J. (2000) The Probabilistic Method, 2nd edn, Wiley, New York.
3. Bollobás, B. and Erdos, P. (1976) On a Ramsey-Turán type problem. J. Combin. Theory Ser. B 21 166-168.
4. Burr, S. A. and Erdos, P. (1975) On the magnitude of generalized Ramsey numbers for graphs. In Infinite and Finite Sets I, Vol. 10 of Colloquia Mathematica Soc. Janos Bolyai, North-Holland, Amsterdam/London, pp. 214-240.
5. Chen, G. and Schelp, R. H. (1993) Graphs with linearly bounded Ramsey numbers. J. Combin. Theory Ser. B 57 138-149.
6. Chvátal, C., Rödl, V., Szemerédi, E. and Trotter, W. T. (1983) The Ramsey number of a graph with bounded maximum degree. J. Combin. Theory Ser. B 34 239-243.
7. Duke, R. A., Erdos, P. and Rödl, V. Intersectionresults for small families. To appear in Random Struct. Alg.
8. Eaton, N. (1998) Ramsey numbers for sparse graphs. Discrete Math. 185 63-75.
9. Graham, R. L., Rödl, V. and Ruciński, A. (2000) On graphs with linear Ramsey numbers. J. Graph Theory 35 176-192.
10. Graham, R. L., Rödl, V. and Ruciński, A. (2001) On bipartite graphs with linear Ramsey numbers. Combinatorica 21 199-209.
11. Kleitman, D. J. (1966) On a combinatorial conjecture of Erdos. J. Combin. Theory 1 209-214.
12. Kostochka, A. and Rödl, V. (2001) On graphs with small Ramsey numbers. J. Graph Theory 37 198-204.
13. Kostochka, A. V. and Rödl, V. On graphswith small Ramsey numbers II. To appear in Combinatorica.
14. Rödl, V. and Thomas, R. (1997) Arrangeability and clique subdivisions. In The Mathematics of Paul Erdos (R. Graham and J. Nešetřil, eds), Vol. 2, Springer, Berlin, pp. 236-239.
15. Sudakov, B. (2003) A few remarks on Ramsey-Turán-type problems. J. Combin. Theory Ser. B 88 99-106.