The paper deals with common generalizations of classical results of Ramsey and Turán. The following is one of the main results. Assumek≧2, ε>0,G n is a sequence of graphs ofn-vertices and at least 1/2((3k−5) / (3k−2)+ε)n 2 edges, and the size of the largest independent set inG n iso(n). LetH be any graph of arboricity at mostk. Then there exists ann 0 such that allG n withn>n 0 contain a copy ofH. This result is best possible in caseH=K 2k .
AMS subject classification (1980)05 C 55 05 C 35
Unable to display preview. Download preview PDF.
- W. Brown andM. Simonovits, Preprint.Google Scholar
- P. Erdős, Graph Theory and Probability,Canadian J. Math. Journal of Mathematics 11 (1959), 34–38.Google Scholar
- P. Erdős andVera T. Sós, Some remarks on Ramsey’s and Turán’s theorem.Coll. Math. Soc. J. Bolyai,4.Comb. Theory and its Appl., North-Holland (1969), 395–404.Google Scholar
- P. Erdős andVera T. Sós, Problems and results on Ramsey—Turán type theorems,Proc. West Coast Conf. on Combinatorics, Graph Th. and Computing, Humboldt State Univ. Arcata (1979), 17–23.Google Scholar
- P. Erdős andVera T. Sós, Problems and results on Ramsey—Turán type theorems II,Studia Sci. Math. Hung. 14 (1979), 27–36.Google Scholar
- Vera T. Sós, On extremal problems in graph theory,Comb. structures and their appl. Proc. Calgary International Conference, Calgary (1969), 407–410.Google Scholar
- E. Szemerédi, Graphs without complete quadrilaterals (in Hungarian),Mat. Lapok 23 (1973), 113–116.Google Scholar
- E. Szemerédi, Regular partitions of graphs,Coll. internat. C. N. R. S. 260 Probl. Combin. et Th. Graphes (1978), 399–402.Google Scholar