On coverings

On category of co-coverings

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

On Finite Lattice Coverings

We consider nite lattice coverings of strictly convex bodies K. For planar centrally symmetric K we characterize the nite arrangements Cn such that conv Cn Cn + K, where Cn is a subset of a covering lattice for K (which satisses some natural conditions). We prove that for a xed lattice the optimal arrangement (measured with the parametric density) is either a sausage, a socalled double sausage ...

On Extension of Coverings

We address the question of when a covering of the boundary of a surface F can be extended to a covering of the surface (equivalently: when is there a branched cover with a prescribedmonodromy ). If such an extension is possible, when can the total space be taken to be connected? When can the extension be taken to be regular? We give necessary and sufficient conditions for both finite and infini...

On biclique coverings

It was proved by Fronček, Jerebic, Klavžar, and Kovář that if a complete bipartite graph Kn,n with a perfect matching removed can be covered by k bicliques, then n ≤ ( k b k 2 c ) . We give a slightly simplified proof and we show that the result is tight. Moreover we use the result to prove analogous bounds for coverings of some other classes of graphs by bicliques. ∗Supported by the University...

Some Theorems on Coverings