Contiguity orders

  • Vincent Bouchitté
  • Abdelmajid Hilali
  • Roland Jégou
  • Jean-Xavier Rampon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1120)


This paper is devoted to the study of contiguity orders i.e. orders having a linear extension L such that all upper (or lower) cover sets are intervals of L. This new class appears to be a strict generalization of both interval orders and N-free orders, and is linearly recognizable. It is proved that computing the number of contiguity extensions is #P-complete, and that the dimension of height one contiguity orders is polynomially tractable. Moreover the membership is a comparability invariant on bi-contiguity orders.


Total Order Linear Extension Interval Order Hasse Diagram Irreducible Element 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Vincent Bouchitté
    • 1
  • Abdelmajid Hilali
    • 2
  • Roland Jégou
    • 3
  • Jean-Xavier Rampon
    • 4
  1. 1.LIP, CNRS URA 1398Ecole Normale Supérieure de LyonLyon Cédex 07France
  2. 2.Groupe L.M.D.I.-I.M.I.Université Claude Bernard-Lyon 1Villeurbanne CédexFrance
  3. 3.Centre SIMADEEcole des Mines de Saint-EtienneSaint-Etienne Cédex 2France
  4. 4.IRISARennes CédexFrance

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