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RSA

2008

2008

For a graph property P, the edit distance of a graph G from P, denoted EP (G), is the minimum number of edge modifications (additions or deletions) one needs to apply to G in order to turn it into a graph satisfying P. What is the furthest graph on n vertices from P and what is the largest possible edit distance from P? Denote this maximal distance by ed(n, P). This question is motivated by algorithmic edge-modification problems, in which one wishes to find or approximate the value of EP (G) given an input graph G. A monotone graph property is closed under removal of edges and vertices. Trivially, for any monotone property, the largest edit distance is attained by a complete graph. We show that this is a simple instance of a much broader phenomenon. A hereditary graph property is closed under removal of vertices. We prove that for any hereditary graph property P, a random graph with an edge density that depends on P essentially achieves the maximal distance from P, that is: ed(n, P) =...

Related Content

Added |
28 Dec 2010 |

Updated |
28 Dec 2010 |

Type |
Journal |

Year |
2008 |

Where |
RSA |

Authors |
Noga Alon, Uri Stav |

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