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 |
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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. |
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ISSN: | 0020-0190 1872-6119 |
DOI: | 10.1016/j.ipl.2012.07.001 |