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The Range of a Random Walk on a Comb

János Pach, Gábor Tardos

The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of the neighbors of ...

Electronic Journal Of Combinatorics2013

Graph-Constrained Group Testing

Amin Karbasi, Mahdi Cheraghchi Bashi Astaneh, Soheil Mohajerzefreh

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most

d

d ...

2012

Graph-Constrained Group Testing

Amin Karbasi, Mahdi Cheraghchi Bashi Astaneh, Soheil Mohajerzefreh

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools and identifying defective items based on tests obtained for each pool. Motivated by applications in network tomography, sensor networks and infection propagati ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 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

Characterizing Path Graphs by Forbidden Induced Subgraphs

A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are mini ...

2009

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

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

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

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

Some combinatorial optimization problems in graphs with applications in telecommunications and tomography

David Schindl

The common point between the different chapters of the present work is graph theory. We investigate some well known graph theory problems, and some which arise from more specific applications. In the first chapter, we deal with the maximum stable set probl ...

EPFL2004

Graph-Constrained Group Testing

Amin Karbasi, Mahdi Cheraghchi Bashi Astaneh, Soheil Mohajerzefreh

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most

d

d ...

2012

Graph-Constrained Group Testing

Amin Karbasi, Mahdi Cheraghchi Bashi Astaneh, Soheil Mohajerzefreh

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools and identifying defective items based on tests obtained for each pool. Motivated by applications in network tomography, sensor networks and infection propagati ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010