Concept

Chromatic polynomial

Related publications (32)

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Applications of a New Separator Theorem for String Graphs

János Pach

An intersection graph of curves in the plane is called a string graph. Matousek almost completely settled a conjecture of the authors by showing that every string graph with m edges admits a vertex separator of size O(root m log m). In the present note, th ...

Cambridge University Press2014

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

Coloring Triangle-Free Rectangular Frame Intersection Graphs with O(loglogn) Colors

Bartosz Maria Walczak

Recently, Pawlik et al. have shown that triangle-free intersection graphs of line segments in the plane can have arbitrarily large chromatic number. Specifically, they construct triangle-free segment intersection graphs with chromatic number Θ(log log n). ...

2013

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

Hardness of Vertex Deletion and Project Scheduling

Ola Nils Anders Svensson

Assuming the Unique Games Conjecture, we show strong inapproximability results for two natural vertex deletion problems on directed graphs: for any integer k ≥ 2 and arbitrary small ε > 0, the Feedback Vertex Set problem and the DAG Vertex Deletion problem ...

Springer2012

A Large-Scale Multi-Lingual Color Thesaurus

Sabine Süsstrunk, Albrecht Johannes Lindner, Bryan Zhi Li

We present a color thesaurus with over 9000 color names in ten different languages. Instead of using conventional psychophysical experiments, we use a statistical framework that is based on search results from Google Image Search. For each color name we co ...

2012

Coloring K-k-free intersection graphs of geometric objects in the plane

János Pach

The intersection graph of a collection C of sets is the graph on the vertex set C, in which C-1 . C-2 is an element of C are joined by an edge if and only if C-1 boolean AND C-2 not equal empty set. Erdos conjectured that the chromatic number of triangle-f ...

2012

IMPEDANCE EFFECTS IN THE CLIC DAMPING RINGS

Nicolas Frank Mounet, Eirini Koukovini Platia, Benoît Salvant, Giovanni Rumolo

Due to the unprecedented brilliance of the beams, the performance of the Compact Linear Collider (CLIC) damping rings (DR) is affected by collective effects. Single bunch instability thresholds based on a broad-band resonator model and the associated coher ...

2011

Beyond Graphs: A New Synthesis

Dario Floreano, Claudio Mattiussi, Daniel Marbach, Peter Dürr

Artiﬁcial neural networks, electronic circuits, and gene networks are some examples of systems that can be modeled as networks, that is, as collections of interconnected nodes. In this paper we introduce the concept of terminal graph (t-graph for short), w ...

2011

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