LOCALLY SEMICOMPLETE DIGRAPHS THAT ARE COMPLEMENTARY M-PANCYCLIC

If A and B are two subdigraphs of D, then we denote by d(D)(A, B) the distance between A and B. Let D be a 2-connected locally semicomplete digraph on n greater than or equal to 6 vertices. If S is a minimum se parating set of D and d = min{d(D-S)(N+(s) - S, N-(s) - S)\s is an ele ment of S}, then m = max{3, d + 2} less than or equal to n/2 and D con tains two vertex-disjoint dicycles of lengths t and n - t for every in teger t satisfying m less than or equal to t less than or equal to n/2 , unless D is a member of a family of locally semicomplete digraphs. T his result extends those of Reid (Ann. Discrete Math. 27 (1985), 321-3 34) and Song (J. Combin. Theory B 57 (1993), 18-25) for tournaments, a nd it confirms two conjectures of Bang-Jensen (Discrete Math. 100 (199 2), 243-265). (C) 1996 John Wiley & Sons, Inc.