Two subsets A,B of an n-element ground set X are said to be crossing, if none of the four sets AB, A\B, B\A and X(AB) are empty. It was conjectured by Karzanov and Lomonosov forty years ago that if a family F of subsets of X does not contain k pairwise cr ...
A family of subsets of {1, ... , n} is called intersecting if any two of its sets intersect. A classical result in extremal combinatorics due to Erdos, Ko and Rado determines the maximum size of an intersecting family of k-subsets of {1, ... , n}. In this ...
A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...
In this paper we study a question related to the classical Erdos-Ko-Rado theorem, which states that any family of k-element subsets of the set [n] = {1,..., n} in which any two sets intersect has cardinality at most ((n-1)(k-1)). We say that two non-empty ...
For integers n >= s >= 2 let e (n, s) denote the maximum of vertical bar F vertical bar, where F is a family of subsets of an n- element set and F contains no s pairwise disjoint members. Half a century ago, solving a conjecture of Erd. os, Kleitman determ ...
