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Graph Transformations preserving the stability number

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Some coloring and walking problems in graphs

Benjamin Leroy-Beaulieu

Graph theory is an important topic in discrete mathematics. It is particularly interesting because it has a wide range of applications. Among the main problems in graph theory, we shall mention the following ones: graph coloring and the Hamiltonian circuit ...

EPFL2008

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

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

Densification Arising from Sampling Fixed Graphs

Matthias Grossglauser, Pedram Pedarsani

During the past decade, a number of different studies have identified several peculiar properties of networks that arise from a diverse universe, ranging from social to computer networks. A recently observed feature is known as network densification, which ...

ACM2008

Deprogramming Large Software Systems

George Candea, Yohann Coppel

Developers turn ideas, designs and patterns into source code, then compile the source code into executables. Decompiling turns executables back into source code, and deprogramming turns code back into designs and patterns. In this paper we introduce DeP, a ...

2008

Automated Delineation of Dendritic Networks in Noisy Image Stacks

Pascal Fua, François Fleuret, Germán González Serrano

We present a novel approach to 3D delineation of dendritic networks in noisy image stacks. We achieve a level of automation beyond that of state-of-the-art systems, which model dendrites as continuous tubular structures and postulate simple appearance mode ...

Springer-Verlag2008

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

Bicolored matchings in some classes of graphs

Dominique de Werra, Bernard Ries

We consider the problem of finding in a graph a set

R

of edges to be colored in red so that there are maximum matchings having some prescribed numbers of red edges. For regular bipartite graphs with

n

nodes on each side, we give sufficient conditions f ...

2007

Robust Routing for Dynamic Wireless Networks Based on Stable Embeddings

Matthias Grossglauser, Suhas Diggavi, Dominique Florian Tschopp, Jörg Widmer

Routing packets is a central function of multi-hop wireless networks. Traditionally, there have been two paradigms for routing, either based on the geographical coordinates of the nodes (geographic routing), or based on the connectivity graph (topology-bas ...

2007

Some graph products and their expansion properties

Mohammad Amin Shokrollahi, Andrew Brown

We introduce "derandomized" versions of the tensor product and the zig-zag product, extending the ideas in the derandomized squaring operation of Rozenman and Vadhan. These enable us to obtain graphs with smaller degrees than those obtained using their non ...

2006

Bicolored matchings in some classes of graphs

Dominique de Werra, Bernard Ries

We consider the problem of finding in a graph a set

R

of edges to be colored in red so that there are maximum matchings having some prescribed numbers of red edges. For regular bipartite graphs with

n

nodes on each side, we give sufficient conditions f ...

2007