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Graphs and Combinatorics

, Volume 22, Issue 4, pp 443–452 | Cite as

Almost Symmetric Cycles in Large Digraphs

  • Lech AdamusEmail author
  • A. Paweł Wojda
Article
  • 40 Downloads

Abstract

We prove that every digraph D with n≥7, nOpen image in new window +6 vertices and at least (nk−1)(n−1)+k(k+1) arcs contains all symmetric cycles of length at most nk−2, an almost symmetric cycle of length nk−1, and with some exceptions, also an almost symmetric cycle of length nk. Consequently, D contains all orientations of cycles of length at most nk, unless D is an exception.

Keywords

Graph Digraph Cycle Orientation of cycle Symmetric cycle 

AMS Subject Classification

05C20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Faculty of Applied MathematicsAGH University of Science and Technology Al.KrakówPoland

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