Thèse de doctorat en Informatique
Sous la direction de Marie-Christine Costa.
Soutenue en 2008
à CNAM .
Pas de résumé disponible.
Mutlcut and induced subgraph problems ; complexity and alggorithms
In this thesis, we consider some problems of graph theory. First, we deal with cut and multicut probems and then, we study induced subgrpah problems. Nevertheless, these two parts share a common purpose : detremining a general overview of the cimplexity of theses problems by proving NP-completeness results or by d"esigning polynomial algrotithms with low running times. In the first part, we tackle cut and multicut problems. We study the consequences of the addition of a cardinality constraint and show the NP-completeness of the general cases. Besides, we give complexity results for some particular graphs such as directed stars and undirected paths, and for the polynomial cases, we design several algorithms using dynamic programming or lagrangian relaxations. Next, we generalize these problems by considering multicriteria versions of the (multi)cut problems. We obtain some NP-completeness results in some very specific classes of graphs like undirected paths and cycles. In the secon part, we focus on the detection of specific induced subgraphs. More precisely, we look for induced paths, induced cycles or induced trees covering a given set of vertices. After proving the NP-completeness of the general cases, we consider the cases where the number of prescribed vertives is fixed. Finally , we also some structural results for C3 free graphs.