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COMBINATORICS
2004
108views more  COMBINATORICS 2004»
13 years 4 months ago
On the Chromatic Number of Intersection Graphs of Convex Sets in the Plane
Let G be the intersection graph of a finite family of convex sets obtained by translations of a fixed convex set in the plane. We show that every such graph with clique number k i...
Seog-Jin Kim, Alexandr V. Kostochka, Kittikorn Nak...
DAM
2007
108views more  DAM 2007»
13 years 4 months ago
3D-interval-filament graphs
: Gavril [GA4] defined two new families of intersection graphs: the interval-filament graphs and the subtree-filament graphs. The complements of intervalfilament graphs are the coi...
Fanica Gavril
JGT
2008
107views more  JGT 2008»
13 years 4 months ago
On planar intersection graphs with forbidden subgraphs
Let C be a family of n compact connected sets in the plane, whose intersection graph G(C) has no complete bipartite subgraph with k vertices in each of its classes. Then G(C) has ...
János Pach, Micha Sharir
CORR
2006
Springer
144views Education» more  CORR 2006»
13 years 4 months ago
The minimum linear arrangement problem on proper interval graphs
We present a linear time algorithm for the minimum linear arrangement problem on proper interval graphs. The obtained ordering is a 4-approximation for general interval graphs. 1 ...
Ilya Safro
WADS
2007
Springer
180views Algorithms» more  WADS 2007»
13 years 10 months ago
Spanners for Geometric Intersection Graphs
A ball graph is an intersection graph of a set of balls with arbitrary radii. Given a real number t > 1, we say that a subgraph G′ of a graph G is a t-spanner of G, if for eve...
Martin Fürer, Shiva Prasad Kasiviswanathan
IV
2009
IEEE
191views Visualization» more  IV 2009»
13 years 11 months ago
An Heuristic for the Construction of Intersection Graphs
Most methods for generating Euler diagrams describe the detection of the general structure of the final draw as the first and most important step. This information is often depi...
Paolo Simonetto, David Auber