Cycle factors in strongly connected local tournaments

ALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS

Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...

Longest paths through an arc in strongly connected in-tournaments

An in-tournament is an oriented graph such that the in-neighborhood of every vertex induces a tournament. Recently, we have shown that every arc of a strongly connected tournament of order n is contained in a directed path of order r(n + 3)/21. This is no longer valid for strongly connected in-tournaments, because there exist examples containing an arc with the property that the longest directe...

On the number of nonseparating vertices in strongly connected local tournaments

algebras with cycle-finite strongly simply connected galois coverings

let $a$ be a nite dimensional $k-$algebra and $r$ be a locally bounded category such that $r rightarrow r/g = a$ is a galois covering dened by the action of a torsion-free group of automorphisms of $r$. following [30], we provide criteria on the convex subcategories of a strongly simply connected category r in order to be a cycle- nite category and describe the module category of $a$. we pro...

Local Tournaments and In - Tournaments

Preface Tournaments constitute perhaps the most well-studied class of directed graphs. One of the reasons for the interest in the theory of tournaments is the monograph Topics on Tournaments [58] by Moon published in 1968, covering all results on tournaments known up to this time. In particular, three results deserve special mention: in 1934 Rédei [60] proved that every tournament has a directe...