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226,148
Intersection Graphs for String Links
, 2003
"... We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graphs, and show that these weight systems are related to the weight systems in ..."
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Cited by 4 (3 self)
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We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graphs, and show that these weight systems are related to the weight systems
Convex Polygon Intersection Graphs
, 2010
"... Geometric intersection graphs are graphs determined by the intersections of certain geometric objects. We study the complexity of visualizing an arrangement of objects that induces a given intersection graph. We give a general framework for describing classes of geometric intersection graphs, using ..."
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Cited by 1 (0 self)
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Geometric intersection graphs are graphs determined by the intersections of certain geometric objects. We study the complexity of visualizing an arrangement of objects that induces a given intersection graph. We give a general framework for describing classes of geometric intersection graphs, using
An Heuristic for the Construction of Intersection Graphs
 13TH INTERNATIONAL CONFERENCE ON INFORMATION VISUALISATION (IV09), BARCELONA: SPAIN
, 2009
"... Most methods for generating Euler diagrams describe the detection of the general structure of the final drawing as the first step. This information is generally encoded using a graph, where nodes are the regions to be represented and edges represent adjacency. A planar drawing of this graph will the ..."
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Cited by 3 (0 self)
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will then indicate how to draw the sets in order to depict all the set intersections. In this paper we present an heuristic to construct this structure, the intersection graph. The final Euler diagram can be constructed by drawing the sets boundaries around the nodes of the intersection graph, either manually
Domination in Geometric Intersection Graphs
 Proc. LATIN 2008, LNCS 4957
, 2008
"... Abstract. For intersection graphs of disks and other fat objects, polynomialtime approximation schemes are known for the independent set and vertex cover problems, but the existing techniques were not able to deal with the dominating set problem except in the special case of unitsize objects. We ..."
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Cited by 6 (1 self)
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Abstract. For intersection graphs of disks and other fat objects, polynomialtime approximation schemes are known for the independent set and vertex cover problems, but the existing techniques were not able to deal with the dominating set problem except in the special case of unitsize objects. We
Some results on the intersection graphs . . .
, 2010
"... Let R be a ring with unity and I(R) ∗ be the set of all nontrivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R) ∗ and two distinct vertices I and J are adjacent if and only if I ∩ J 6 = 0. In this paper, we study some connections betw ..."
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Let R be a ring with unity and I(R) ∗ be the set of all nontrivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R) ∗ and two distinct vertices I and J are adjacent if and only if I ∩ J 6 = 0. In this paper, we study some connections
Mutant knots and intersection graphs
, 2007
"... We prove that if a finite order knot invariant does not distinguish mutant knots, then the corresponding weight system depends on the intersection graph of a chord diagram rather than on the diagram itself. The converse statement is easy and well known. We discuss relationship between our results an ..."
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Cited by 4 (0 self)
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We prove that if a finite order knot invariant does not distinguish mutant knots, then the corresponding weight system depends on the intersection graph of a chord diagram rather than on the diagram itself. The converse statement is easy and well known. We discuss relationship between our results
Intersection graphs of segments and ∃R
, 2014
"... A graph G with vertex set {v1, v2,..., vn} is an intersection graph of segments if there are segments s1,..., sn in the plane such that si and sj have a common point if and only if {vi, vj} is an edge of G. In this expository paper, we consider the algorithmic problem of testing whether a given abst ..."
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Cited by 8 (0 self)
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A graph G with vertex set {v1, v2,..., vn} is an intersection graph of segments if there are segments s1,..., sn in the plane such that si and sj have a common point if and only if {vi, vj} is an edge of G. In this expository paper, we consider the algorithmic problem of testing whether a given
Intersection Graphs of Pseudosegments: Chordal Graphs
, 2010
"... We investigate which chordal graphs have a representation as intersection graphs of pseudosegments. For positive we have a construction which shows that all chordal graphs that can be represented as intersection graphs of subpaths on a tree are pseudosegment intersection graphs. We then study the li ..."
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Cited by 3 (0 self)
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We investigate which chordal graphs have a representation as intersection graphs of pseudosegments. For positive we have a construction which shows that all chordal graphs that can be represented as intersection graphs of subpaths on a tree are pseudosegment intersection graphs. We then study
Chordal Graphs as Intersection Graphs of pseudosegments
"... We investigate which chordal graphs have a representation as intersection graphs of pseudosegments. The main contribution is a construction which shows that all chordal graphs which have a representation as intersection graph of subpaths on a tree are representable. A family of intersection graphs o ..."
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Cited by 1 (1 self)
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We investigate which chordal graphs have a representation as intersection graphs of pseudosegments. The main contribution is a construction which shows that all chordal graphs which have a representation as intersection graph of subpaths on a tree are representable. A family of intersection graphs
Approximation Algorithms for Intersection Graphs
, 2009
"... We introduce three new complexity parameters that in some sense measure how chordallike a graph is. The similarity to chordal graphs is used to construct simple polynomialtime approximation algorithms with constant approximation ratio for many NPhard problems, when restricted to graphs for which ..."
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Cited by 8 (0 self)
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partition for large classes of intersection graphs.
Results 1  10
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226,148