Existence of cyclic k-cycle systems of the complete graph

Authors:
Marco Buratti;Alberto Del Fra
Affiliations:
Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, I-06123 Perugia, Italy;Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma "La Sapienza", Via Scarpa 16, I-00161 Roma, Italy
Venue:
Discrete Mathematics - Papers on the occasion of the 65th birthday of Alex Rosa
Year:
2003

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Abstract

Starting from earliest papers by Rosa we solve, directly and explicitly, the existence problem for cyclic k-cycle systems of the complete graph Kv with v ≡ 1 (mod 2k), and the existence problem for cyclic k-cycle systems of the complete m-partite graph Km×k with m and k being odd. As a particular consequence, a cyclic p-cycle system of Kv with p being a prime exists for all admissible values of v but (p,v) ≠ (3,9). This was previously known only for p = 3, 5, 7.