String graph: Difference between revisions

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There is nothing wrong with the references here. Editor seems to on a crusade against anything conflicting with the badly-written Intersection (Line) Graphs of hypergraphs
clean up lede, was very repetitive and somewhat hard to understand
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{{orphan|date=March 2008}}
 
In [[graph theory]], a '''string graph''' is an [[intersection graph]] of [[Curve| stringscurves]] in the plane; each curve is called a plane"string". Given a graph <math>''G</math>'', <math>''G</math>'' is a string graph if and only if there exists a set of curves, or strings, that permit a drawingdrawn in the plane wheresuch that no three strings intersect at thea samesingle point and thesuch setthat ofthe stringsgraph thathaving intersecta isvertex isomorphicfor toeach <math>E(G)</math>.curve Thatand is,an aedge stringfor grapheach isintersecting an intersection graphpair of curves in the plane where each curve is aisomorphic vertexto and each intersection an edge''G''.
 
More formally, <math>G</math> is a string graph if and only if there exists some set of strings <math>S</math> such that the intersection graph
 
: <math>I = (\{ s | s \in S\}, \{(s,t) | s,t \in S \wedge s \cap t \not= \varnothing\})</math>
 
is isomorphic to <math>G</math>. We say that the size of a string graph is equal to the number of intersections, <math>|I|</math>.
 
== Background ==