ON THE EXISTENCE OF (K5 \ e)-DESIGNS WITH APPLICATION TO OPTICAL NETWORKS.

Motivated by the connection between graph decompositions and traffic grooming in optical networks, we continue the investigation of the existence problem for (K₅ \ e)-designs of order n. It is proved that the necessary conditions for the existence of such designs are also sufficient with 3 definite exceptions (n = 9, 10, 18) and 12 possible exceptions with n = 234 being the largest. This gives a near solution for the long standing problem posed by Bermond et al. in [Ars Combin., 10 (1980), pp. 211-254]. As a consequence, we also give an optimal grooming on n nodes with C = 9 when such a (K₅ \e)-design of order n exists. [ABSTRACT FROM AUTHOR]