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ICALP
2011
Springer
9 years 6 months ago
Clique Clustering Yields a PTAS for max-Coloring Interval Graphs
We are given an interval graph G = (V, E) where each interval I ∈ V has a weight wI ∈ R+. The goal is to color the intervals V with an arbitrary number of color classes C1, C2...
Tim Nonner
CORR
2011
Springer
143views Education» more  CORR 2011»
9 years 6 months ago
Polynomial kernels for Proper Interval Completion and related problems
Given a graph G = (V, E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V × V ) \ E such that the graph...
Stéphane Bessy, Anthony Perez
JGT
2010
158views more  JGT 2010»
10 years 1 months ago
Cubicity of interval graphs and the claw number
Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product I1 × I2 × · · · × Ib, where ea...
Abhijin Adiga, L. Sunil Chandran
DM
2007
106views more  DM 2007»
10 years 2 months ago
The Roberts characterization of proper and unit interval graphs
In this note, a constructive proof is given that the classes of proper interval graphs and unit interval graphs coincide, a result originally established by Fred S. Roberts. Addit...
Frédéric Gardi
COR
2007
99views more  COR 2007»
10 years 2 months ago
An improved algorithm for the p-center problem on interval graphs with unit lengths
The p-center problem is to locate p facilities in a network of n demand points so as to minimize the longest distance between a demand point and its nearest facility. We consider ...
T. C. Edwin Cheng, Liying Kang, C. T. Ng
CORR
2008
Springer
71views Education» more  CORR 2008»
10 years 2 months ago
Asteroids in rooted and directed path graphs
An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. Asteroidal triples play a central ...
Kathie Cameron, Chính T. Hoàng, Benj...
ICALP
1995
Springer
10 years 6 months ago
Intervalizing k-Colored Graphs
The problem to determine whether a given k-colored graph is a subgraph of a properly colored interval graph has an application in DNA physical mapping. In this paper, we study the...
Hans L. Bodlaender, Babette de Fluiter
ESA
2000
Springer
104views Algorithms» more  ESA 2000»
10 years 6 months ago
Efficient Algorithms for Centers and Medians in Interval and Circular-Arc Graphs
The p-center problem is to locate p facilities on a network so as to minimize the largest distance from a demand point to its nearest facility. The p-median problem is to locate p ...
Sergei Bespamyatnikh, Binay K. Bhattacharya, J. Ma...
ESA
2009
Springer
109views Algorithms» more  ESA 2009»
10 years 7 months ago
Linear-Time Recognition of Probe Interval Graphs
The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a varia...
Ross M. McConnell, Yahav Nussbaum
ESA
2005
Springer
162views Algorithms» more  ESA 2005»
10 years 8 months ago
Minimal Interval Completions
We study the problem of adding edges to an arbitrary graph so that the resulting graph is an interval graph. Our objective is to add an inclusion minimal set of edges, which means ...
Pinar Heggernes, Karol Suchan, Ioan Todinca, Yngve...
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