Partitions versus sets: A case of duality

Authors:
Laurent Lyaudet;Frédéric Mazoit;Stéphan Thomassé
Affiliations:
Université d'Orléans - LIFO, Rue Léonard de Vinci, B.P. 6759, F-45067 Orléans Cedex 2, France;Université Bordeaux - LaBRI, 351, cours de la Libration, F-33405 Talence Cedex, France;Université Montpellier II - CNRS, LIRMM, 161 rue Ada, 34392 Montpellier Cedex, France
Venue:
European Journal of Combinatorics
Year:
2010

Citing 4
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Abstract

In a recent paper, Amini et al. introduced a general framework to prove duality theorems between tree-decompositions and their dual combinatorial object. They unify all known ad hoc proofs in one duality theorem based on submodular partition functions. This general theorem remains however a bit technical and relies on this particular submodularity property. Instead of partition functions, we propose here a simple combinatorial property of a set of partitions which also gives these duality results. Our approach is both simpler, and a little bit more general.