On graphs with linear Ramsey numbers

Journal of Graph Theory

Volumn 35, Issue 3, 2000, Pages 176-192

  Graham, R L ^a   Rodl V ^b   Rucinski A ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b EMORY UNIVERSITY   (United States)

^c ADAM MICKIEWICZ UNIVERSITY   (Poland)

Author keywords

Graph embeddings; Maximum degree; Probabilistic method; Ramsey number

Indexed keywords

EID: 0042689505     PISSN: 03649024     EISSN: None     Source Type: Journal    
DOI: 10.1002/1097-0118(200011)35:3<176::AID-JGT3>3.0.CO;2-C     Document Type: Article

References (18)

1. N. Alon, Subdivided graphs have linear Ramsey numbers, J. Graph Theory 18 (1994), 343-347.
2. J. Beck, An upper bound for diagonal Ramsey numbers, Studia Sci. Math. Hungar. 18 (1983), 401-406.
3. S. A. Burr and P. Erdös, On the magnitude of generalized Ramsey numbers for graphs, Coll. Math. Soc. Janós Bolyai 10, Infinite and Finite Sets, North Holland, Amsterdam, 1975, 214-240.
4. S. A. Burr, P. Erdös, and J. H. Spencer, Ramsey theorems for multiple copies of graphs, Trans. Am. Math. Soc. 209 (1975), 87-99.
5. G. Chen and R. Schelp, Graphs with linearly bounded Ramsey numbers, J. Combin. Theory (B) 57 (1993), 138-149.
6. V. Chvatál, V. Rödl, E. Szemerédi, and W. T. Trotter Jr, The Ramsey number of a graph with bounded maximum degree, J. Combin. Theory (B) 34 (1983), 239-243.
7. N. Eaton, Ramsey numbers for sparse graphs, Discrete Math 185 (1998), 63-75.
8. W. T. Gowers, Lower bounds of tower type for Szemerédi's uniformity lemma, GAFA, Geom. Funct. Anal. 7 (1997), 322-337.
9. R. L. Graham, B. L. Rothschild, and J. H. Spencer, Ramsey Theory, 2nd ed., John Wiley & Sons, New York, 1990.
10. S. Janson, T. Luczal, and A. Ruciński, Random Graphs, John Wiley & Sons, New York, 2000.
11. H. A. Kierstead and W. T. Trotter, Planar graph coloring with an uncooperative partner, DIMACS Series in Discrete Math, and Theor. Comp. Sci. 9 (1993), 85-93.
12. Y. Kohayakawa, H.-J. Prömel, and V. Rödl, Induced Ramsey numbers, Combinatorica 18 (1998), 373-404.
13. J. Komlós, M. Simonovits, Szemeredi's regularity lemma and its applications in graph theory, Combinatorics, Paul Erdös is Eighty (Volume 2), Keszthely (Hungary), 1993, Budapest (1996), 295-352.
14. A. Kostochka and V. Rödl, On graphs with small Ramsey numbers, submitted.
15. V. Rödl and R. Thomas, Arrangeability and clique subdivisions, The Mathematics of Paul Erdös, R. L. Graham and J. Nešetřil, (editors), Springer Verlag, Heidelberg, 1997, 236-239.
16. N. Sauer and J. H. Spencer, Edge disjoint placements of graph, J. Combin. Theory (B) 25 (1978), 295-302.
17. E. Szemerédi, Regular partitions of graphs, Problèmes combinatoires et théorie des graphes, Orsay 1976, J.-C. Bermond, J.-C. Fournier, M. Las Vergnas, and D. Sotteau, (Editors), Colloq. Internat. CNRS 260, Paris, 1978, 399-401.
18. R. L. Graham, V. Rödl, and A. Ruciński, On bipartite graphs with linear Ramsey numbers, Combinatorica, to appear.