Order

, Volume 8, Issue 1, pp 49–61

Cycle-free partial orders and chordal comparability graphs

  • Tze-Heng Ma
  • Jeremy P. Spinrad
Article

Abstract

This paper studies a number of problems on cycle-free partial orders and chordal comparability graphs. The dimension of a cycle-free partial order is shown to be at most 4. A linear time algorithm is presented for determining whether a chordal directed graph is transitive, which yields an O(n2) algorithm for recognizing chordal comparability graphs. An algorithm is presented for determining whether the transitive closure of a digraph is a cycle-free partial order in O(n+mt)time, where mtis the number of edges in the transitive closure.

AMS subject classifications (1991)

Primary 06A06 secondary 05C20 68Q25 

Key words

Partial order cycle-free poset chordal comparability graph poset dimension algorithm transitive closure 

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Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Tze-Heng Ma
    • 1
  • Jeremy P. Spinrad
    • 2
  1. 1.Institute of Information ScienceAcademia SinicaTaipeiPeople's Republic of China
  2. 2.Department of Computer ScienceVanderbilt UniversityNashvilleUSA

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