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Generalized vertex coloring problems using split graphs

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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

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

A graph coloring heuristic using partial solutions and a reactive tabu scheme

Nicolas Zufferey

Most of the recent heuristics for the graph coloring problem start from an infeasible k-coloring (adjacent vertices may have the same color) and try to make the solution feasible through a sequence of color exchanges. In contrast, our approach (called FOO- ...

2008

The stable set polytope of quasi-line graphs

Friedrich Eisenbrand, Gautier Stauffer

It is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even n ...

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

Wavelets on Graphs via Spectral Graph Theory

Pierre Vandergheynst, Rémi Gribonval

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite graph. We define a notion of scaling using the graph analogue of the Fourier domain, namely the space of eigenfunctions forming the sp ...

2008

Complexity of mixed graph coloring

Bernard Ries

In this note we consider two coloring problems in mixed graphs, i.e., graphs containing edges and arcs. We show that they are both

\mathcal{NP}

-complete in cubic planar bipartite graphs. This answers an open question from \cite{Ries2}. ...

2008

Variable space search for graph coloring

Nicolas Zufferey, Matthieu Plumettaz

Let G = (V, E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1, ..., k}) to each vertex of G so that no edge has both endpoints with the same color. We propose a new local search methodology, ...

2008

Graph colouring approaches for a satellite range scheduling problem

Nicolas Zufferey, Patrick Amstutz, Philippe Giaccari

A goal of this paper is to efficiently adapt the best ingredients of the graph colouring techniques to an NP-hard satellite range scheduling problem, called MuRRSP. We propose two new heuristics for the MuRRSP, where as many jobs as possible have to be sch ...

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

Complexity of mixed graph coloring

Bernard Ries

In this note we consider two coloring problems in mixed graphs, i.e., graphs containing edges and arcs. We show that they are both

\mathcal{NP}

-complete in cubic planar bipartite graphs. This answers an open question from \cite{Ries2}. ...

2008