We study the consequences of introducing individual nonconformity in social interactions, based on Axelrod’s model for the dissemination of culture. A constraint on the number of situations in which interaction may take place is introduced in order to lift the unavoidable homogeneity present in the final configurations arising in Axelrod’s related models. The inclusion of this constraint leads ...

The Tur\'an number $\text{ex}(n,H)$ of a graph $H$ is the maximal edges in an $H$-free on $n$ vertices. In $1983$ Chung and Erd\H{o}s asked which graphs with $e$ minimize $\text{ex}(n,H)$. They resolved this question asymptotically for most range to complete picture. paper we answer their by resolving all remaining cases. Our result translates directly setting universality, well-studied notion ...

Let Dk denote the tournament on 3k vertices consisting of three disjoint vertex classes V1, V2 and V3 of size k, each oriented as a transitive subtournament, and with edges directed from V1 to V2, from V2 to V3 and from V3 to V1. Fox and Sudakov proved that given a natural number k and ǫ > 0 there is n0(k, ǫ) such that every tournament of order n ≥ n0(k, ǫ) which is ǫ-far from being transitive ...

The notion of an unavoidable set of words appears frequently in the fields of mathematics and theoretical computer science, in particular with its connection to the study of combinatorics on words. The theory of unavoidable sets has seen extensive study over the past twenty years. In this paper we extend the definition of unavoidable sets of words to unavoidable sets of partial words. Partial w...