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On a graph coloring problem arising from discrete tomography

Publications associées (45)

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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

On some coloring problems in grids

Dominique de Werra

We study complexity issues related to some coloring problems in grids: we examine in particular the case of List coloring, of Precoloring extension and of (p, q)-List coloring, the case of List coloring in bipartite graphs where lists in the first part of ...

2013

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

Every graph admits an unambiguous bold drawing

János Pach

Let r and w be a fixed positive numbers, w < r. In a bold drawing of a graph, every vertex is represented by a disk of radius r, and every edge by a narrow rectangle of width w. We solve a problem of van Kreveld [K09] by showing that every graph admits a b ...

Springer-Verlag Berlin2011

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

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

An Optimal Linear-Time Algorithm for Interprocedural Register Allocation in High Level Synthesis Using SSA Form

Paolo Ienne, Philip Brisk, Ajay Kumar Verma

An optimal linear-time algorithm for interprocedural register allocation in high level synthesis is presented. Historically, register allocation has been modeled as a graph coloring problem, which is nondeterministic polynomial time-complete in general; ho ...

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

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

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

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