Prechains and self duality

Boudabbous, Youssef; Delhommé, Christian

doi:10.1016/j.disc.2012.01.025

Cited by 8 publications

(16 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Une préchaîne (dite prechain dans [6]) est un digraphe, n'ayant ni pic, ni diamant, et dont les éventuelles paires neutres sont deux à deux disjointes. Considérons quelques préchaînes particulières, qui seront utilisées dans nos principaux résultats.…”

unclassified

See 1 more Smart Citation

{−1}-self dual finite prechains and applications

Bouchaala

Boudabbous

Lopez

2013

Comptes Rendus. Mathématique

Self Cite

View full text Add to dashboard Cite

unclassified

“…On appelle roue faible (dite weak wheel dans [6]), tout digraphe appartenant à la réunion des classes S n , où n 1.…”

unclassified

{−1}-self dual finite prechains and applications

Bouchaala

Boudabbous

Lopez

2013

Comptes Rendus. Mathématique

Self Cite

View full text Add to dashboard Cite

“…In this subsection, we give the definition and some properties of prechains. The prechains were introduced by Y. Boudabbous and C. Delhommé in [13], where they studied the (≤ k)-self converse (finite or infinite) digraphs where k ≥ 4. Notice that the prechains were motivated by the morphology of the difference classes of two (≤ 4)-isomorphic digraphs which was obtained by G. Lopez and C. Rauzy in 1992 [30], and that we will recall in the next subsection.…”

Section: Prechainsmentioning

confidence: 99%

“…The following proposition is a consequence of the above description. The complete list of small arc-connected and hereditarily self converse digraphs is given in [9,13].…”

Section: Hereditarily Self Converse Digraphsmentioning

confidence: 99%

See 1 more Smart Citation

Two {4,n-3}-isomorphic n-vertex digraphs are hereditarily isomorphic

Boudabbous

2019

Filomat

Self Cite

View full text Add to dashboard Cite

Let D and D be two digraphs with the same vertex set V, and let F be a set of positive integers. The digraphs D and D are hereditarily isomorphic whenever the (induced) subdigraphs D[X] and D [X] are isomorphic for each nonempty vertex subset X. They are F-isomorphic if the subdigraphs D[X] and D [X] are isomorphic for each vertex subset X with | X |∈ F. In this paper, we prove that if D and D are two {4, n − 3}-isomorphic n-vertex digraphs, where n ≥ 9, then D and D are hereditarily isomorphic. As a corollary, we obtain that given integers k and n with 4 ≤ k ≤ n − 6, if D and D are two {n − k}-isomorphic n-vertex digraphs, then D and D are hereditarily isomorphic. To the memory of my dear master Gérard LOPEZ who taught me and gave me the passion of reconstruction. With all my gratitude and admiration. 1. Introduction All digraphs mentioned here are finite, and have no loops and no multiple edges. Thus a digraph (or directed graph) D consists of a nonempty and finite set V(D) of vertices with a collection E(D) of ordered pairs of distinct vertices, called the set of edges of D. Such a digraph is denoted by (V(D), E(D)). We recall the basic notions of the reconstruction problem in the theory of relations what we apply to the case of digraphs. Consider two digraphs D and D on the same vertex set V with |V| = n ≥ 1, and let k be a positive integer. The digraphs D and D are hereditarily isomorphic if the subdigraphs D[X] and D [X], induced on X, are isomorphic for each nonempty subset X of V. They are k-isomorphic whenever for every k-element vertex subset X, the subdigraphs D[X] and D [X] are isomorphic. They are (≤ k)-isomorphic if they are k-isomorphic for every positive integer k with k ≤ k. The digraphs D and D are (−k)-isomorphic whenever either k ≥ n or D and D are (n − k)-isomorphic with k < n. Let F be a set of non zero integers. The digraphs D and D are F-isomorphic whenever D and D are p-isomorphic for every p ∈ F. The digraph D is F-reconstructible if every digraph F-isomorphic to D is 2010 Mathematics Subject Classification. 05C20;05C60

show abstract

A Proof of the Alternate Thomassé Conjecture for Countable N-Free Posets

Abdi

2023

Order

View full text Add to dashboard Cite

Prechains and self duality

Cited by 8 publications

References 11 publications

{−1}-self dual finite prechains and applications

{−1}-self dual finite prechains and applications

Two {4,n-3}-isomorphic n-vertex digraphs are hereditarily isomorphic

A Proof of the Alternate Thomassé Conjecture for Countable N-Free Posets

Contact Info

Product

Resources

About