论文信息 - On finite set-systems whose every intersection is a Kernel of a star

On finite set-systems whose every intersection is a Kernel of a star

Let k, t be positive integers and let F be a set-system which consists of k-element sets. In this paper it is proved that one can choose a subsystem F^*@?F containing a positive proportion of the members of F, (i.e |F^*| > c(k,t) |F|) and having the property that every pairwise intersection is a kernel of a t-star in F^* (i.e. @?, F'@e F^*, FtnF' = A, @eF"1, ..., F"t @e F^* such that F"i @? F"j = A for 1 =

Zoltán Füredi | Z. Füredi

[1] Peter Frankl. Families of finite sets with prescribed cardinalities for pairwise intersections , 1980 .

[2] Peter Frankl. Families of finite sets with three intersections , 1984, Comb..

[3] Peter Frankl,et al. On Set Intersections , 1980, J. Comb. Theory, Ser. A.

[4] Paul Erdös,et al. On the combinatorial problems which I would most like to see solved , 1981, Comb..

[5] Peter Frankl,et al. A Finite Set Intersection Theorem , 1981, Eur. J. Comb..

[6] P. Erdös,et al. On coloring graphs to maximize the proportion of multicolored k-edges , 1968 .

[7] P. Erdös,et al. Intersection Theorems for Systems of Sets , 1960 .