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Recognizing Threshold Tolerance Graphs in \(O(n^2)\) Time

  • Petr A. Golovach
  • Pinar Heggernes
  • Nathan LindzeyEmail author
  • Ross M. McConnell
  • Vinícius Fernandes dos Santos
  • Jeremy P. Spinrad
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8747)

Abstract

A graph \(G = (V,E)\) is a threshold tolerance graph if each vertex \(v \in V\) can be assigned a weight \(w_v\) and a tolerance \(t_v\) such that two vertices \(x,y \in V\) are adjacent if \(w_x + w_y \ge \min (t_x,t_y)\). Currently, the most efficient recognition algorithm for threshold tolerance graphs is the algorithm of Monma, Reed, and Trotter which has an \(O(n^4)\) runtime. We give an \(O(n^2)\) algorithm for recognizing threshold tolerance and their complements, the co-threshold tolerance (co-TT) graphs, resolving an open question of Golumbic, Weingarten, and Limouzy.

Keywords

Interval Graph Chordal Graph Complete Subgraph Interval Model Split Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Petr A. Golovach
    • 1
  • Pinar Heggernes
    • 1
  • Nathan Lindzey
    • 2
    Email author
  • Ross M. McConnell
    • 3
  • Vinícius Fernandes dos Santos
    • 4
  • Jeremy P. Spinrad
    • 5
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Mathematics DepartmentColorado State UniversityFort CollinsUSA
  3. 3.Computer Science DepartmentColorado State UniversityFort CollinsUSA
  4. 4.Departamento de Matematica AplicadaUniversidade do Estado do Rio de Janeiro - UERJRio de JaneiroBrazil
  5. 5.Department of Electrical Engineering and Computer ScienceVanderbilt UniversityNashvilleUSA

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