Pancyclic out-arcs of a vertex in oriented graphs

Authors:
Qiaoping Guo;Shengjia Li;Ruijuan Li;Gaokui Xu
Affiliations:
School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China;Institute of Mathematics and Applied Mathematics, Shanxi University, Taiyuan 030006, China;Institute of Mathematics and Applied Mathematics, Shanxi University, Taiyuan 030006, China;School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China
Venue:
Information Processing Letters
Year:
2012

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Abstract

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 d"D^+(x)+d"D^-(y)=n-3. Song (1994) [5] proved that D is pancyclic. Bang-Jensen and Guo (1999) [2] proved, based on Song@?s 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.