Intersection graphs of rectangles and segments

Authors:
R. Ahlswede;I. Karapetyan
Affiliations:
Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany;-
Venue:
General Theory of Information Transfer and Combinatorics
Year:
2006

Citing 2
Cited 4

Some combinatorial problems

Discrete Mathematics
Covering boxes by points

Discrete Mathematics

Coloring kk-free intersection graphs of geometric objects in the plane

Proceedings of the twenty-fourth annual symposium on Computational geometry
Coloring and maximum independent set of rectangles

APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Coloring Kk-free intersection graphs of geometric objects in the plane

European Journal of Combinatorics
Approximating hitting sets of axis-parallel rectangles intersecting a monotone curve

Computational Geometry: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let F be a finite family of sets and G(F) be the intersection graph of F (the vertices of G(F) are the sets of family F and the edges of G(F) correspond to intersecting pairs of sets). The transversal number τ(F) is the minimum number of points meeting all sets of F. The independent (stability) number α(F) is the maximum number of pairwise disjoint sets in F. The clique number ω(F) is the maximum number of pairwise intersecting sets in F. The coloring number q(F) is the minimum number of classes in a partition of F into pairwise disjoint sets.