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Finding H -partitions efficiently

Simone Dantas, Celina M. H. de Figueiredo, Sylvain Gravier, Sulamita Klein (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We study the concept of an H -partition of the vertex set of a graph G , which includes all vertex partitioning problems into four parts which we require to be nonempty with only external constraints according to the structure of a model graph H , with the exception of two cases, one that has already been classified as polynomial, and the other one remains unclassified. In the context of more general vertex-partition problems, the problems addressed in this paper have these properties: non-list, 4 -part,...

Finding H-partitions efficiently

Simone Dantas, Celina M.H. de Figueiredo, Sylvain Gravier, Sulamita Klein (2010)

RAIRO - Theoretical Informatics and Applications

We study the concept of an H-partition of the vertex set of a graph G, which includes all vertex partitioning problems into four parts which we require to be nonempty with only external constraints according to the structure of a model graph H, with the exception of two cases, one that has already been classified as polynomial, and the other one remains unclassified. In the context of more general vertex-partition problems, the problems addressed in this paper have these properties: non-list, 4-part, external...

Full approximability of a class of problems over power sets.

Giorgio Ausiello, Alberto Marchetti-Spaccamela, Marco Protasi (1981)

Qüestiió

In this paper results concerning structural and approximability properties of the subclass of NP-Complete Optimization Problems, defined over a lattice are considered. First, various approaches to the concept of Fully Polynomial Approximation Scheme are presented with application to several known problems in the class of NP-Complete Optimization Problems.Secondly, a characterization of full Approximability for the class of Max Subset Problems is introduced.

Generalized polar varieties and an efficient real elimination

Bernd Bank, Marc Giusti, Joos Heintz, Luis M. Pardo (2004)

Kybernetika

Let W be a closed algebraic subvariety of the n -dimensional projective space over the complex or real numbers and suppose that W is non-empty and equidimensional. In this paper we generalize the classic notion of polar variety of W associated with a given linear subvariety of the ambient space of W . As particular instances of this new notion of generalized polar variety we reobtain the classic ones and two new types of polar varieties, called dual and (in case that W is affine) conic. We show that...

Hardness Results for Total Rainbow Connection of Graphs

Lily Chen, Bofeng Huo, Yingbin Ma (2016)

Discussiones Mathematicae Graph Theory

A total-colored path is total rainbow if both its edges and internal vertices have distinct colors. The total rainbow connection number of a connected graph G, denoted by trc(G), is the smallest number of colors that are needed in a total-coloring of G in order to make G total rainbow connected, that is, any two vertices of G are connected by a total rainbow path. In this paper, we study the computational complexity of total rainbow connection of graphs. We show that deciding whether a given total-coloring...

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