Abstract
We prove that every digraph D with n≥7, n≥
+6 vertices and at least (n−k−1)(n−1)+k(k+1) arcs contains all symmetric cycles of length at most n−k−2, an almost symmetric cycle of length n−k−1, and with some exceptions, also an almost symmetric cycle of length n−k. Consequently, D contains all orientations of cycles of length at most n−k, unless D is an exception.
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The research was partially supported by the AGH University of Science and Technology grant No 11 420 04
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Adamus, L., Wojda, A. Almost Symmetric Cycles in Large Digraphs. Graphs and Combinatorics 22, 443–452 (2006). https://doi.org/10.1007/s00373-006-0668-x
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DOI: https://doi.org/10.1007/s00373-006-0668-x