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Coloring K-k-free intersection graphs of geometric objects in the plane

Publications associées (41)

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Variations of coloring problems related to scheduling and discrete tomography

Bernard Ries

The graph coloring problem is one of the most famous problems in graph theory and has a large range of applications. It consists in coloring the vertices of an undirected graph with a given number of colors such that two adjacent vertices get different col ...

EPFL2007

Constrained paths in the flip-graph of regular triangulations

Thomas Liebling, Lionel Pournin

We describe particular paths in the flip-graph of regular triangulations in any dimension. It is shown that any pair of regular triangulations is connected by a path along which none of their common faces are destroyed. As a consequence, we obtain the conn ...

2007

Generalized vertex coloring problems using split graphs

Tinaz Ekim

Graph theory experienced a remarkable increase of interest among the scientific community during the last decades. The vertex coloring problem (Min Coloring) deserves a particular attention rince it has been able to capture a wide variety of applications. ...

EPFL2006

(k,lambda)-colorings and universal graphs

Ivo Blöchliger, Daniela Bronner

We consider vertex k-colorings of an arbitrary simple, connected, and undirected graph G=(V,E) such that, for every vertex v, at most lambda different colors occur in the closed neighborhood of v. These colorings are called (k,lambda)-colorings. If a graph ...

2006

On the stable set polytope of claw-free graphs

Gautier Stauffer

In this thesis we focus our attention on the stable set polytope of claw-free graphs. This problem has been open for many years and albeit all the efforts engaged during those last three years, it is still open. This does not mean that no progress has been ...

EPFL2005

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 graph ...

2005

Partitioning cographs into cliques and stable sets

Dominique de Werra, Tinaz Ekim

We consider the problem of partitioning the node set of a graph into p cliques and k stable sets, namely the (p,k)-coloring problem. Results have been obtained for general graphs \cite{hellcomp}, chordal graphs \cite{hellchordal} and cacti for the case whe ...

2005

Circular Ones Matrices and the Stable set Polytopes 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 ...

2005

Circular Ones Matrices and the Stable Set Polytope of Quasi-Line Graphs

Friedrich Eisenbrand, Gautier Stauffer

2004

The Winding Road toward a Characterization of the Stable Set Polytope

Thomas Liebling, Gautier Stauffer

We survey results about the facial structure of the stable set polytope for variants of claw-free graphs. ...

2004