Publication

Online Coloring of Comparability Graphs: some results

Related publications (38)

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Triangle-free intersection graphs of line segments with large chromatic number

Bartosz Maria Walczak, Michal Lason

In the 1970s Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer k we construct a triangle-free fam ...

Academic Press Inc Elsevier Science2014

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

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 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

Intersection Patterns of Edges in Topological Graphs

Radoslav Fulek

This thesis is devoted to crossing patterns of edges in topological graphs. We consider the following four problems: A thrackle is a graph drawn in the plane such that every pair of edges meet exactly once: either at a common endpoint or in a proper crossi ...

EPFL2012

Coloring fuzzy circular interval graphs

Friedrich Eisenbrand, Martin Niemeier

Given a graph G with nonnegative node labels w, a multiset of stable sets S_1,...,S_k\subseteq V(G) such that each vertex v \in V(G) is contained in w(v) many of these stable sets is called a weighted coloring. The weighted coloring number \chi_w(G) is the ...

Elsevier2012

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

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