Results 1  10
of
68
On the Intersection of Tolerance and Cocomparability Graphs
"... Tolerance graphs have been extensively studied since their introduction, due to their interesting structure and their numerous applications, as they generalize both interval and permutation graphs in a natural way. It has been conjectured by Golumbic, Monma, and Trotter in 1984 that the intersection ..."
Abstract
 Add to MetaCart
that the intersection of tolerance and cocomparability graphs coincides with bounded tolerance graphs. Since cocomparability graphs can be efficiently recognized, a positive answer to this conjecture in the general case would enable us to efficiently distinguish between tolerance and bounded tolerance graphs, although
On the Intersection of Tolerance and Cocomparability Graphs
"... Abstract. It has been conjectured by Golumbic and Monma in 1984 that the intersection of tolerance and cocomparability graphs coincides with bounded tolerance graphs. Since cocomparability graphs can be efficiently recognized, a positive answer to this conjecture in the general case would enable us ..."
Abstract
 Add to MetaCart
Abstract. It has been conjectured by Golumbic and Monma in 1984 that the intersection of tolerance and cocomparability graphs coincides with bounded tolerance graphs. Since cocomparability graphs can be efficiently recognized, a positive answer to this conjecture in the general case would enable us
Domination in Bounded Interval Tolerance Graphs
"... In this paper we present efficient algorithms to solve domination set problem for the class of bounded tolerance graphs. The class of bounded tolerance graphs includes interval graphs and permtation graph as subclasses. Our solution to domination set problem has improved bounds for time complexity t ..."
Abstract
 Add to MetaCart
than the algorithm for the general cocomparability graphs which can as well be used for bounded tolerance graphs.
A New Intersection Model and Improved Algorithms for Tolerance Graphs
, 2009
"... Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This class of graphs, which generalizes in a natural way both interval and permutation graphs, has attracted many research efforts since their introduction in [ ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
in [10], as it finds many important applications in constraintbased temporal reasoning, resource allocation, and scheduling problems, among others. In this article we propose the first nontrivial intersection model for general tolerance graphs, given by threedimensional parallelepipeds, which extends
Tolerance Graphs and Orders
 J. Graph Theory
"... We show that if a tolerance graph is the complement of a comparability graph it is a trapezoid graph, i.e., the complement of an order of interval dimension at most 2. As consequences we are able to give obstructions for the class of bounded tolerance graphs and to give an example of a graph which i ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
We show that if a tolerance graph is the complement of a comparability graph it is a trapezoid graph, i.e., the complement of an order of interval dimension at most 2. As consequences we are able to give obstructions for the class of bounded tolerance graphs and to give an example of a graph which
An Intersection Model for Multitolerance Graphs: Efficient Algorithms and Hierarchy
"... Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This class of graphs has attracted many research efforts, mainly due to its interesting structure and its numerous applications, especially in DNA sequence analy ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
set problem on tolerance graphs, thus closing the complexity gap for this problem. Additionally, by exploiting more the new 3Dintersection model, we completely classify multitolerance graphs in the hierarchy of perfect graphs.
Max PointTolerance Graphs
"... A graph G is a max pointtolerance (MPT) graph if each vertex v of G can be mapped to a pointedinterval (Iv, pv) where Iv is an interval of R and pv ∈ Iv such that uv is an edge of G iff Iu ∩ Iv ⊇ {pu, pv}. MPT graphs model relationships among DNA fragments in genomewide association studies as wel ..."
Abstract
 Add to MetaCart
A graph G is a max pointtolerance (MPT) graph if each vertex v of G can be mapped to a pointedinterval (Iv, pv) where Iv is an interval of R and pv ∈ Iv such that uv is an edge of G iff Iu ∩ Iv ⊇ {pu, pv}. MPT graphs model relationships among DNA fragments in genomewide association studies
THE RECOGNITION OF TOLERANCE AND BOUNDED TOLERANCE GRAPHS
, 2010
"... Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure and its numerous applications. Several efficient algorithms ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure and its numerous applications. Several efficient
The Recognition of Tolerance and Bounded Tolerance Graphs is NPcomplete
, 2009
"... Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This class of graphs has been extensively studied, due to both its interesting structure and its numerous applications (in bioinformatics, constrainedbased tem ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This class of graphs has been extensively studied, due to both its interesting structure and its numerous applications (in bioinformatics, constrained
Proper and unit tolerance graphs DISCRETE APPLIED
, 1991
"... We answer a question of Golumbic, Monma and Trotter by constructing proper tolerance graphs that are not unit tolerance graphs. An infinite family of graphs that are minimal in this respect is specified. 1. ..."
Abstract
 Add to MetaCart
We answer a question of Golumbic, Monma and Trotter by constructing proper tolerance graphs that are not unit tolerance graphs. An infinite family of graphs that are minimal in this respect is specified. 1.
Results 1  10
of
68