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The splittance of a graph

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Abstract

The splittance of an arbitrary graph is the minimum number of edges to be added or removed in order to produce a split graph (i.e. a graph whose vertex set can be partitioned into a clique and an independent set). The splittance is seen to depend only on the degree sequence of the graph, and an explicit formula for it is derived. This result allows to give a simple characterization of the degree sequences of split graphs. Worst cases for the splittance are determined for some classes of graphs (the class of all graphs, of all trees and of all planar graphs).

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Authors and Affiliations

  1. University of Waterloo, Ont., Canada

    Peter L. Hammer & Bruno Simeone

  2. Instituto per le Applicazioni del Calcolo, Rome, Italy

    Peter L. Hammer & Bruno Simeone

Authors
  1. Peter L. Hammer
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  2. Bruno Simeone
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Hammer, P.L., Simeone, B. The splittance of a graph. Combinatorica 1, 275–284 (1981). https://doi.org/10.1007/BF02579333

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  • DOI: https://doi.org/10.1007/BF02579333

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