Locally semicomplete digraphs that are complementarym-pancyclic
Yubao Guo, Lutz Volkmann · Journal of Graph Theory · 1996
If A and B are two subdigraphs of D, then we denote by dD (A, B) the distance between A and B. Let D be a 2-connected locally semicomplete digraph on n ≥ 6 vertices. If S is a minimum separating set of D and then m = max{3, d + 2} ≤ n/2 and D contains two vertex-disjoint dicycles of lengths t and n − t for every integer t satisfying m ≤ t ≤ n/2, unless D is a member of a family of locally semicomplete digraphs. This result extends those of Reid (Ann. Discrete Math. 27 (1985), 321–334) and Song (J. Combin. Theory B 57 (1993), 18–25) for tournaments, and it confirms two conjectures of Bang-Jensen (Discrete Math. 100 (1992), 243–265. © 1996 John Wiley & Sons, Inc.