Almost resolvable cycle systems—an analogue of Hanani triple systems

The purpose of this paper is the initiation of an attack on the general existence problem for almost resolvable 2 k ‐cycle systems. We give a complete solution for 2 k =6 as well as a complete solution modulo one possible exception for 2 k =10 and 14. We also show that the existence question for almost resolvable 2 k ‐cycle systems can be settled if we can show the existence for the two smallest possible orders 4 k +1 and 8 k +1. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 404–410, 2009