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Average-case analysis of dynamic graph algorithms

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Graphs that Admit Right Angle Crossing Drawings

Radoslav Fulek, Balázs Keszegh, Filip Moric

We consider right angle crossing (RAC) drawings of graphs in which the edges are represented by polygonal arcs and any two edges can cross only at a right angle. We show that if a graph with n vertices admits a RAC drawing with at most 1 bend or 2 bends pe ...

2010

k-Edge-Connectivity: Approximation and LP Relaxation

David Pritchard

This paper's focus is the following family of problems, denoted k-ECSS, where k denotes a positive integer: given a graph (V, E) and costs for each edge, find a minimum-cost subset F of E such that (V, F) is k-edge-connected. For k=1 it is the spanning tre ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010

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

Degenerate crossing numbers

János Pach

Let G be a graph with n vertices and ea parts per thousand yen4n edges, drawn in the plane in such a way that if two or more edges (arcs) share an interior point p, then they properly cross one another at p. It is shown that the number of crossing points, ...

Springer-Verlag2009

The Holt-Klee condition for oriented matroids

Holt and Klee have recently shown that every (generic) LP orientation of the graph of a d-polytope satisfies a directed version of the d-connectivity property, i.e. there are d internally disjoint directed paths from a unique source to a unique sink. We in ...

2009

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

A Strategy Based on Maximum Spanning Trees to Stitch Together Microscope Images

Michaël Unser, Philippe Thévenaz

Assembling partial views is an attractive means to extend the field of view of microscope images. In this paper, we propose a semi-automated solution to achieve this goal. Its intended audience is the microscopist who desires to scan a large area while acq ...

SPIE2006

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