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Ramsey numbers of ordered graphs

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Adjacent Crossings Do Matter

Radoslav Fulek

In a drawing of a graph, two edges form an odd pair if they cross each other an odd number of times. A pair of edges is independent if they share no endpoint. For a graph G, let ocr(G) be the smallest number of odd pairs in a drawing of G and let iocr(G) b ...

Springer-Verlag Berlin2011

Chemical Hieroglyphs: Abstract Depiction of Complex Void Space Topology of Nanoporous Materials

Berend Smit

In general, most porous materials are so complex that structural information cannot be easily observed with 3D visualization tools. To address this problem, we have developed a special abstract 2D representation to depict all important topological features ...

2010

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

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. ...

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

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

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

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

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

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