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International Conference on Formal Concept Analysis

ICFCA 2013: Formal Concept Analysis pp 44–59Cite as

Dismantlable Lattices in the Mirror

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7880))

Abstract

We investigate properties which hold for both the lattice of a binary relation and for its ’mirror lattice’, which is the lattice of the complement relation.

We first prove that the relations whose lattice is dismantlable corres-pond to the class of chordal bipartite graphs; we provide algorithmic tools to find a doubly irreducible element in such a lattice.

We go on to show that a lattice is dismantlable and its mirror lattice is also dismantlable if and only if both these lattices are planar.

Research partially supported by the French Agency for Research under the DEFIS program TODO, ANR-09-EMER-010.

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Author information

Authors and Affiliations

  1. LIMOS UMR CNRS 6158, Ensemble Scientifique des Cézeaux, Université Blaise Pascal, 63 173, Aubière, France

    Anne Berry & Alain Sigayret

Authors
  1. Anne Berry
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  2. Alain Sigayret
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Editor information

Editors and Affiliations

  1. IRISA, 263 avenue du Général Leclerc, 35042, Rennes, France

    Peggy Cellier

  2. Computer Science Department, TU Dresden, Nöthnitzer Str. 46, 01062, Dresden, Germany

    Felix Distel

  3. Department of Mathematics, TU Dresden, Zellescher Weg 12-14, 01062, Dresden, Germany

    Bernhard Ganter

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Berry, A., Sigayret, A. (2013). Dismantlable Lattices in the Mirror. In: Cellier, P., Distel, F., Ganter, B. (eds) Formal Concept Analysis. ICFCA 2013. Lecture Notes in Computer Science(), vol 7880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38317-5_3

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  • DOI: https://doi.org/10.1007/978-3-642-38317-5_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38316-8

  • Online ISBN: 978-3-642-38317-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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