HEREDITARY HEMIMORPHY OF {-κ}-HEMIMORPHIC TOURNAMENTS FOR ≥ 5

Bouaziz, Moncef; Boudabbous, Youssef; Amri, Nadia El

doi:10.4134/JKMS.2011.48.3.599

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HEREDITARY HEMIMORPHY OF {-κ}-HEMIMORPHIC TOURNAMENTS FOR ≥ 5

Journal title : Journal of the Korean Mathematical Society
Volume 48, Issue 3, 2011, pp.599-626
Publisher : The Korean Mathematical Society
DOI : 10.4134/JKMS.2011.48.3.599

Title & Authors

HEREDITARY HEMIMORPHY OF {-κ}-HEMIMORPHIC TOURNAMENTS FOR ≥ 5
Bouaziz, Moncef; Boudabbous, Youssef; Amri, Nadia El;

Abstract

Let T = (V,A) be a tournament. With every subset X of V is associated the subtournament T[X] = (X, A ${${\cap}$}$ (X ${${\times}$}$ X)) of T, induced by X. The dual of T, denoted by ${$T^*$}$ , is the tournament obtained from T by reversing all its arcs. Given a tournament T' = (V,A') and a non-negative integer ${${\kappa}$}$ , T and T' are { ${$-{\kappa}$}$ }-hemimorphic provided that for all X ${${\subset}$}$ V, with ${${\mid}X{\mid}$}$ = ${${\kappa}$}$ , T[V-X] and T'[V-X] or ${$T^*$}$ [V-X] and T'[V-X] are isomorphic. The tournaments T and T' are said to be hereditarily hemimorphic if for all subset X of V, the subtournaments T[X] and T'[X] are hemimorphic. The purpose of this paper is to establish the hereditary hemimorphy of the { ${$-{\kappa}$}$ }-hemimorphic tournaments on at least k + 7 vertices, for every ${${\kappa}{\geq}5$}$ .

Keywords

tournament;isomorphy;hereditary isomorphy;hemimorphy;hereditary hemimorphy;

Language

English

Cited by

3time(s) in CrossRef

Description of the Tournaments Which are Reconstructible from Their k-cycle Partial Digraphs for $$k \in \{3, 4\}$$ k ∈ { 3 , 4 }, Graphs and Combinatorics, 2016, 32, 5, 1881

The (⩽6)-half-reconstructibility of digraphs, Comptes Rendus Mathematique, 2014, 352, 7-8, 541

Les paires de tournois -hypomorphes, Comptes Rendus Mathematique, 2012, 350, 9-10, 433

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