A family of r sets is called a 2-system if any two sets have the same intersection. Denote by F(n, r) the most number of subsets of an n-element set which do not contain a 2-system consisting of râ€¦ (More)

Let A be a finite matrix with integral entries and G be an Abelian group . Define A to be partition regular in G if for every partition of G\{0} into finitely many classes there exist elements xl , .â€¦ (More)

Recently, in conversation with ErdÅ‘s, Hajnal asked whether or not for any triangle-free graph G on the vertex set N, there always exists a sequence ã€ˆxnã€‰n=1 so that whenever F and H are distinctâ€¦ (More)

We present some necessary and su cient conditions (in terms of degrees of vertices) for locally nite tree T=(V; E) to be paradoxical, i.e. to have a partition V=V1âˆªV2 and one-to-one mappings fi :V â†’â€¦ (More)