Algoritmos E Comdexidade De

of Thesis presented to COPPE/UFRJ as partia1 fulfillment of the requirements for the degree of Doctor of Science (D.Sc.) Algorithms and Cornplexity of Graph Decomposition Sulamita Klein October, 1994 Thesis Supervisors : Jayme Luiz Szwarcfiter Department : Computing and Systems Engineering We study some types of graph decompositions. Initially, we consider the decoinposition induced by the existence of a homogeneous set in a graph. We present an O(n3) time algorithm which determines if a graph admits a homogeneous set. Secondly, we consider the decomposition induced by the existence of a homogeneous pair in a graph. Hoinogeneous pairs are natural generalizations of homogeneous sets. We present an O(n5) time algorithm which determines if a giaph adrnits a homogeneous pair. We also study clique decompositions of a graph, with some restrictions given a priori. We consider a particular case called clique-cross partition and we develop a linear algorithm which determines if a graph admits such partition. We discuss some recognition problems of graphs with certain cutsets, such as cliclue cutset, star cutset, stable cutset, skew cutset and others. We show that tlie problem STABLE CUTSET and the problem MULTIPARTITE CUTSET are NP-complete.