This survey is intended to be a fast (and reasonably updated) reference for the theory of Stallings automata and its applications to the study of subgroups of the free group, with the main accent on algorithmic aspects. ...

A famous theorem of Dirac states that any graph on n vertices with minimum degree at least n/2 has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this result, we show the existence of rainbow Hamilton ...

Freiman’s 2.4-Theorem states that any set A¿Zp satisfying |2A|=2.4|A|-3 and |A|<p/35 can be covered by an arithmetic progression of length at most |2A|-|A|+1. A more general result of Green and Ruzsa implies that this ...

We prove that an additive code over a finite field which has a few projections which are equivalent to a linear code is itself equivalent to a linear code, providing the code is not too short.

Let A and B be randomly chosen s-subsets of the first n integers such that their sumset A+B has size at most Ks. We show that asymptotically almost surely A and B are almost fully contained in arithmetic progressions PA ...

The purpose of this paper is to study the properties of the irrational-slope Thompson’s group Ft introduced by Cleary in [11]. We construct presentations, both finite and infinite, and we describe its combinatorial structure ...

To an arc A of PG(k-1,q) of size q+k-1-t we associate a tensor in ¿¿k,t(A)¿¿k-1 , where ¿k,t denotes the Veronese map of degree t defined on PG(k-1,q) . As a corollary we prove that for each arc A in PG(k-1,q) of size ...

Given a countably infinite hypergraph $\mathcal R$ and a finite hypergraph $\mathcal A$, the \emph{big Ramsey degree} of $\mathcal A$ in $\mathcal R$ isthe least number $L$ such that, for every finite $k$ and every ...

Given $t\ge 2$ and $0\le k\le t$, we prove that the number of labelled $k$-connected chordal graphs with $n$ vertices and tree-width at most $t$ is asymptotically $c n^{-5/2} \gamma^n n!$, as $n\to\infty$, for some constants ...