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54
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 ..."
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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 ..."
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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 ..."
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than the algorithm for the general cocomparability graphs which can as well be used for bounded tolerance graphs.
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 ..."
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Cited by 4 (3 self)
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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.
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 ..."
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Cited by 4 (4 self)
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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
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. ..."
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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.
Vertex Splitting and the Recognition of Trapezoid Graphs
, 2009
"... Trapezoid graphs are the intersection family of trapezoids where every trapezoid has a pair of opposite sides lying on two parallel lines. These graphs have received considerable attention and lie strictly between permutation graphs (where the trapezoids are lines) and cocomparability graphs (the c ..."
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Cited by 8 (3 self)
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Trapezoid graphs are the intersection family of trapezoids where every trapezoid has a pair of opposite sides lying on two parallel lines. These graphs have received considerable attention and lie strictly between permutation graphs (where the trapezoids are lines) and cocomparability graphs (the
An Encounter with Graphs
, 2006
"... So far diagnosis of some problems we came across during our works with algorithms, graphs played significant roles. In this paper, we have tried to show that graphs really occupy a major role in computer science and engineering. The abstraction of problems as different graph models as well as graphs ..."
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So far diagnosis of some problems we came across during our works with algorithms, graphs played significant roles. In this paper, we have tried to show that graphs really occupy a major role in computer science and engineering. The abstraction of problems as different graph models as well
The Recognition of Geodetically Connected Graphs
, 1998
"... Let G = (V, E) be a graph with vertex set V of size n and edge set E of size m. A vertex v 2 V is called a hinge vertex if the distance of any two vertices becomes longer after v is removed. A graph without hinge vertex is called a hingefree graph. In general, a graph G is kgeodetically connected ..."
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Cited by 2 (1 self)
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or kGC for short if G can tolerate any k,1vertices failures without increasing the distance among all the remaining vertices. In this paper, we show that recognizing a graph G to be kGC for the largest value of k can be solved in O(nm) time. In addition, more efficient algorithms for recognizing
Kayles on special classes of graphs  An application of SpragueGrundy theory
 IN PROCEEDINGS OF THE 18TH INTERNATIONAL WORKSHOP ON GRAPHTHEORETIC CONCEPTS IN COMPUTER SCIENCE, WG'92
, 1993
"... Kayles is the game, where two players alternately choose a vertex that has not been chosen before nor is adjacent to an already chosen vertex from a given graph. The last player that choses a vertex wins the game. We show, with help of SpragueGrundy theory, that the problem to determine which playe ..."
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Cited by 1 (1 self)
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player has a winning strategy for a given graph, can be solved in O(n³) time on interval graphs, on circular arc graphs, on permutation graphs, and on cocomparability graphs and in O(n^1.631) time on cographs. For general graphs, the problem is known to be PSPACEcomplete, but can be solved in time
Results 1  10
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54