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Network coding as a coloring problem (Invited paper)

Related publications (32)

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Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

Bartosz Maria Walczak, Michal Lason

Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the ...

Springer US2013

Iterative Coding for Network Coding

Rüdiger Urbanke, Andrea Montanari

We consider communication over a noisy network under randomized linear network coding. Possible error mechanisms include node-or link-failures, Byzantine behavior of nodes, or an overestimate of the network min-cut. Building on the work of Kotter and Kschi ...

Ieee-Inst Electrical Electronics Engineers Inc2013

On coloring problems with local constraints

Yuri Faenza

We deal with some generalizations of the graph coloring problem on classes of perfect graphs. Namely we consider the μ-coloring problem (upper bounds for the color on each vertex), the precoloring extension problem (a subset of vertices colored beforehand) ...

Elsevier2012

A note on chromatic properties of threshold graphs

Dominique de Werra, Bernard Ries, Rico Zenklusen

In threshold graphs one may find weights for the vertices and a threshold value t such that for any subset S of vertices, the sum of the weights is at most the threshold t if and only if the set S is a stable (independent) set. In this note we ask a simila ...

2012

Universal Sets for Straight-Line Embeddings of Bicolored Graphs

Jan Kyncl

A set S of n points is 2-color universal for a graph G on n vertices if for every proper 2-coloring of G and for every 2-coloring of S with the same sizes of color classes as G has, G is straight-line embeddable on S. We show that the so-called double chai ...

2011

The potential to improve the choice: list conflict-free coloring for geometric hypergraphs

Shakhar Smorodinsky

Given a geometric hypergraph (or a range-space)

H=(V,\cal E)

, a coloring of its vertices is said to be conflict-free if for every hyperedge

S \in \cal E

there is at least one vertex in

S

whose color is distinct from the colors of all other vertices i ...

2010

Coloring axis-parallel rectangles

János Pach, Gábor Tardos

For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by precisely r members of the family, all of which have the same color. For r = 2, th ...

2010

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

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

Complexity of mixed graph coloring

Bernard Ries

In this note we consider two coloring problems in mixed graphs, i.e., graphs containing edges and arcs. We show that they are both

\mathcal{NP}

-complete in cubic planar bipartite graphs. This answers an open question from \cite{Ries2}. ...

2008

The potential to improve the choice: list conflict-free coloring for geometric hypergraphs

Shakhar Smorodinsky

Given a geometric hypergraph (or a range-space)

H=(V,\cal E)

, a coloring of its vertices is said to be conflict-free if for every hyperedge

S \in \cal E

there is at least one vertex in

S

whose color is distinct from the colors of all other vertices i ...

2010

Complexity of mixed graph coloring

Bernard Ries

In this note we consider two coloring problems in mixed graphs, i.e., graphs containing edges and arcs. We show that they are both

\mathcal{NP}

-complete in cubic planar bipartite graphs. This answers an open question from \cite{Ries2}. ...

2008