(Romanian Society of Applied & Industrial Mathematics Universitatea din Pitesti, 2015) Braguţă, Galina; Cataranciuc, Sergiu
For a complex of multi-ary relations [12] it is defined the concept of (k,m)-chain which is a generalization of the concept of chain known from the graph theory. Using (k,m)- chains it is introduced the concept of the distance function and it is proved that this function generate a convexity in the complex of multi-ary relations. It is operating with the concepts of convexity and convex hull, axiomatically defined by F.Levi [29] and we describe the iterative procedure to construct a convex hull for a subset of elements from the complex of multi-ary relations. [ABSTRACT FROM AUTHOR]
This paper is focused on some aspects of undirected graphs covering, in particular convex sets problem (CCS) and partitioning undirected graph into convex sets problem (PCS). We prove theorems regarding existence of graphs with fxed number of convex sets which serve as solutions to CCS and PCS problems.
