Personne

Dominique de Werra

Publications associées (59)

Blockers and transversals in some subclasses of bipartite graphs: When caterpillars are dancing on a grid

Given an undirected graph G = (V, E) with matching number nu(G), a d-blocker is a subset of edges B such that nu((V, E \ B))

Elsevier2010

On the use of graphs in discrete tomography

Dominique de Werra, Bernard Ries

In this tutorial paper, we consider the basic image reconstruction problem which stems from discrete tomography. We derive a graph theoretical model and we explore some variations and extensions of this model. This allows us to establish connections with s ...

2010

A projective algorithm for preemptive open shop scheduling with two multiprocessor groups

Dominique de Werra

We study a multiprocessor extension of the preemptive open shop scheduling problem, where the set of processors is partitioned into processor groups. We show that the makespan minimization problem is polynomially solvable for two multiprocessor groups even ...

2010

Split-critical and uniquely split-colorable graphs

Dominique de Werra, Bernard Ries, Tinaz Ekim

The split-coloring problem is a generalized vertex coloring problem where we partition the vertices into a minimum number of split graphs. In this paper, we study some notions which are extensively studied for the usual vertex coloring and the cocoloring p ...

2010

Weighted coloring on planar, bipartite and split graphs: Complexity and approximation

Dominique de Werra

We study complexity and approximation of MIN WEIGHTED NODE COLORING in planar, bipartite and split graphs. We show that this problem is NP-hard in planar graphs, even if they are triangle-free and their maximum degree is bounded above by 4. Then, we prove ...

2009

On the inapproximability of independent domination in 2P3-free perfect graphs

Dominique de Werra

We consider the complexity of approximation for the INDEPENDENT DOMINATING SET problem in 2P(3)-free graphs, i.e., graphs that do not contain two disjoint copies of the chordless path on three vertices as all induced subgraph. We show that, if P not equal ...

2009

Graph transformations preserving the stability number

Dominique de Werra

We analyse the relations between several graph transformations that were introduced to be used in procedures determining the stability number of a graph. We show that all these transformations can be decomposed into a sequence of edge deletions and twin de ...

2009

Blockers and transversals

Dominique de Werra, Bernard Ries, Rico Zenklusen

Given an undirected graph G = (V, E) with matching number v(G), we define d-blockers as subsets of edges B such that nu((V, E \ B)) = d. ...

Elsevier2009

A tutorial on the use of graph coloring for some problems in robotics

Dominique de Werra, Tinaz Ekim

We study the problem where a robot has to pick up items of different sizes which are stored along a corridor. A natural requirement is that the items have to be collected in decreasing order of their sizes. We deal with various systems according to the loc ...

2009

From L. Euler to D. König

Dominique de Werra

Starting from the famous Konigsberg bridge problem which Euler described in 1736, we intend to show that some results obtained 180 years later by Konig are very close to Euler's discoveries. ...

2009

Degree-constrained edge partitioning in graphs arising from discrete tomography

Dominique de Werra, Bernard Ries

Starting from the basic problem of reconstructing a 2-dimensional image given by its projections on two axes, one associates a model of edge coloring in a complete bipartite graph. The complexity of the case with k=3 colors is open. Variations and special ...

2009

Graph coloring with cardinality constraints on the neighborhoods

Dominique de Werra, Bernard Ries

Extensions and variations of the basic problem of graph coloring are introduced. The problem consists essentially in finding in a graph G a k-coloring, i.e., a partition V-1,...,V-k of the vertex set of G such that, for some specified neighborhood (N) over ...

2009

A Magnetic Procedure for the Stability Number

Dominique de Werra

A magnet is a pair u, v of adjacent vertices such that the proper neighbours of u are completely linked to the proper neighbours of v. It has been shown that one can reduce the graph by removing the two vertices u, v of a magnet and introducing a new verte ...

2009

Polarity of chordal graphs

Dominique de Werra, Tinaz Ekim

Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. They are defined by the existence of a certain partition of vertices, which is NP-complete to decide for general graphs. It has been recently proved that for cographs, th ...

2008

Finding Hamiltonian circuits in quasi-adjoint graphs

Dominique de Werra, Benjamin Leroy-Beaulieu

This paper is motivated by a method used for DNA sequencing by hybridization presented in [Jacek Blazewicz, Marta Kasprzak, Computational complexity of isothernnic DNA sequencing by hybridization, Discrete Appl. Math. 154 (5) (2006) 718-7291. This paper pr ...

2008

On two coloring problems in mixed graphs

Dominique de Werra, Bernard Ries

We are interested in coloring the vertices of a mixed graph, i.e., a graph containing edges and arcs. We consider two different coloring problems: in the first one we want adjacent vertices to have different colors and the tail of an arc to get a color str ...

2008

Preemptive open shop scheduling with multiprocessors: polynomial cases and applications

Dominique de Werra

This paper addresses a multiprocessor generalization of the preemptive open-shop scheduling problem. The set of processors is partitioned into two groups and the operations of the jobs may require either single processors in either group or simultaneously ...

2008

A tutorial on the use of graphs in discrete tomography

Dominique de Werra, Bernard Ries

Starting from the basic image reconstruction problem in discrete tomography some graph theoretical models are proposed. This suggests the study of some variations and extensions of the basic problem. Applications in scheduling and timetabling are described ...

Springer-Verlag2008

On a graph coloring problem arising from discrete tomography

Dominique de Werra, Bernard Ries

An extension of the basic image reconstruction problem in discrete tomography is considered: given a graph

G=(V,E)

and a family

\mathcal{P}

of chains

P_i

together with vectors

h(P_i)=(h_{i}^{1},...,h_{i}^{k})

, one wants to find a partition $V^{1},. ...

2008

Polar cographs

Dominique de Werra, Tinaz Ekim

Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s, k)-polar if there exists a partition A, B of its vertex set such that A induces a complete s-partite grap ...

Elsevier2008