Intersection theorems on structures

  • Schelp, R. H.; Simonovits, M.; Sós, V. T. Intersection theorems for $t$-valued functions. European J. Combin. 9 (1988), no. 6, 531--536.
  • Simonovits, Miklós; Sós, Vera T.: Intersection properties of subsets of integers. European J. Combin. 2 (1981), no. 4, 363--372.
  • Graham, R. L.; Simonovits, M.; Sós, V. T. A note on the intersection properties of subsets of integers. J. Combin. Theory Ser. A 28 (1980), no. 1, 106--110.
  • Simonovits, Miklós; Sós, Vera T.: Intersection theorems on structures. Combinatorial mathematics, optimal designs and their applications (Proc. Sympos. Combin. Math. and Optimal Design, Colorado State Univ., Fort Collins, Colo., 1978). Ann. Discrete Math. 6 (1980), 301--313.
  • Simonovits, M.; Sós, V. T. Intersection theorems for graphs. II. Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. II, pp. 1017--1030, Colloq. Math. Soc. János Bolyai, 18, North-Holland, Amsterdam-New York, 1978.
  • Simonovits, Miklós; Sós, Vera T.: Intersection theorems for graphs. Problèmes combinatoires et théorie des graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976), pp. 389--391, Colloq. Internat. CNRS, 260, CNRS, Paris, 1978.

Some related papers

  • Faudree, R. J.; Schelp, R. H.; Sos, Vera T.: Some intersection theorems on two-valued functions. Combinatorica 6 (1986), no. 4, 327--333.
  • Erdos, P.; Sos, V. T. Problems and results on intersections of set systems of structural type. Utilitas Math. 29 (1986), 61--70.
  • Chung, F. R. K.; Graham, R. L.; Frankl, P.; Shearer, J. B.: Some intersection theorems for ordered sets and graphs.
  • Szabó, Tibor: Intersection properties of subsets of integers. European J. Combin. 20 (1999), no. 5, 429--444.

Some open problems

The intersection of two graphs on a given vertex set in the graph spanned by the common edges. (Sometimes it is irrelevant, but mostly we delete the isolated vertices.)
  • How many graphs can be given on n vertices if the intersection of any two contains a triangle?
  • How many graphs can be given on n vertices if the intersection of any two is connected?