Pancyclic out-arcs of a vertex in oriented graphs

Let D be an oriented graph with n⩾9 vertices and minimum degree at least n−2, such that, for any two vertices x and y, either x dominates y or dD+(x)+dD−(y)⩾n−3. Song (1994) [5] proved that D is pancyclic. Bang-Jensen and Guo (1999) [2] proved, based on Songʼs result, that D is vertex pancyclic. In...

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Veröffentlicht in:Information processing letters 2012-10, Vol.112 (20), p.759-761
Hauptverfasser: Guo, Qiaoping, Li, Shengjia, Li, Ruijuan, Xu, Gaokui
Format: Artikel
Sprache:eng
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Zusammenfassung:Let D be an oriented graph with n⩾9 vertices and minimum degree at least n−2, such that, for any two vertices x and y, either x dominates y or dD+(x)+dD−(y)⩾n−3. Song (1994) [5] proved that D is pancyclic. Bang-Jensen and Guo (1999) [2] proved, based on Songʼs result, that D is vertex pancyclic. In this article, we give a sufficient condition for D to contain a vertex whose out-arcs are pancyclic in D, when n⩾14. ► We consider out-arc pancyclic vertex in oriented graph. ► We use path-contracting technique to prove our results. ► We give a sufficient condition for an oriented graph to contain an out-arc pancyclic vertex.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2012.07.001