Abstract
Let Lk be the graph formed by the lowest three levels of the Boolean lattice B k , i.e.,V(Lk)={0, 1,...,k, 12, 13,..., (k−1)k} and 0is connected toi for all 1≤i≤k, andij is connected toi andj (1≤i<j≤k).
It is proved that if a graph G overn vertices has at leastk 3/2 n 3/2 edges, then it contains a copy of Lk.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Bollobás,Extremal Graph Theory, Academic Press, London-New York, 1978.
W. G. Brown, On graphs that do not contain a Thomsen graph,Canad. Math. Bull. 9 (1966), 281–289.
D. de Caen, Extension of a theorem of Moon and Moser on complete hypergraphs,Ars Combinatoria,16 (1983), 5–10.
P. Erdős, On some extremal problems in graph theory,Israel J. Math. 3 (1965), 113–116.
P. Erdős, Some recent results on extremal problems in graph theory,Theory of Graphs (Internat. Sympos, Rome, 1966), Gordon and Breach, New York, 1967, 117–130.
P. Erdős, Extremal problems on graphs and hypergraphs,in Hypergraph Seminar (Proc. First Working Sem., Ohio State Univ., Colubmus, Ohio, 1972)Lecture Notes in Math. 411, Springer, Berlin, 1974. pp. 75–84.
P. Erdős, Problems and results on finite and infinite combinatorial analysis,in Infinite and Finite Sets (Proc. Conf. Keszthely, Hungary, 1973.)Proc. Colloq. Math. Soc. J. Bolyai 10 Bolyai-North-Holland, 1975. pp. 403–424.
P. Erdős, A. Rényi andV. T. Sós, On a problem of graph theory,Studia Sci. Math. Hungar. 1 (1966), 215–235.
P. Erdős andM. Simonovits, A limit theorem in graph theory,Studia Sci. Math. Hungar. 1 (1966), 51–57.
P. Erdős andM. Simonovits, Cube-supersaturated graphs and related problems,Progress in graph Theory (Waterloo, Ont. 1982), 203–218. Academic Press, Toronto, Ont., 1984.
P. Erdős andA. H. Stone, On the structure of linear graphs,Bull. Amer. Math. Soc. 52 (1946), 1087–1091.
Z. Füredi, Quadrilateral-free graphs with maximum number of edges,to appear
T. Kővári, V. T. Sós, andP. Turán, On a problem of K. Zarankiewicz,Colloquium Math. 3 (1954), 50–57.
M. Simonovits, Extremal graph problems, degenerate extremal problems, and supersaturated graphs,Progress in graph Theory (Waterloo, Ont. 1982), 419–437. Academic Press, Toronto, Ont., 1984.
Author information
Authors and Affiliations
Additional information
Research supported in part by the Hungarian National Science Foundation under Grant No. 1812