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THE CONVEXITY IN THE COMPLEX OF MULTI-ARY RELATIONS
(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]
ON NONTRIVIAL COVERS AND PARTITIONS OF GRAPHS BY CONVEX SETS
(Institutul de Matematică şi Informatică al Academiei de Ştiinţe a Moldovei, 2018) Buzatu, Radu; Cataranciuc, Sergiu
In this paper we prove that it is NP-complete to decide whet- her a graph can be partitioned into nontrivial convex sets. We show that it can be verified in polynomial time whether a graph can be covered by nontrivial convex sets. Also, we propose a re- cursive formula that establishes the maximum nontrivial convex cover number of a tree.