(≤k)-reconstructible binary relations

Abstract : Abstract A relation R is ( ≤ k ) -reconstructible ( k a positive integer) if it is isomorphic with any relation S on the same vertex set with the property that the relations induced by R and S on any set of at most k vertices are isomorphic; it is ( ≤ k ) -self dual if every restriction to at most k vertices is self dual, i.e.  isomorphic to its dual relation (the relation obtained by reversing its arcs). In particular, relying on the description of ( ≤ k ) -self dual binary relations, we characterize, for each k ≥ 4 , all ( ≤ k ) -reconstructible binary relations: A binary relation is ( ≤ k ) -reconstructible if and only if its modules that are chains are finite and its ( ≤ k ) -self dual modules are self dual.
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European Journal of Combinatorics, Elsevier, 2013, 37, pp.43 - 67. 〈10.1016/j.ejc.2013.07.010〉
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http://hal.univ-reunion.fr/hal-01186137
Contributeur : Nicolas Alarcon <>
Soumis le : lundi 24 août 2015 - 14:27:51
Dernière modification le : vendredi 14 septembre 2018 - 08:16:09

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Youssef Boudabbous, Christian Delhommé. (≤k)-reconstructible binary relations. European Journal of Combinatorics, Elsevier, 2013, 37, pp.43 - 67. 〈10.1016/j.ejc.2013.07.010〉. 〈hal-01186137〉

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