Almost $$2$$ 2 -perfect $$6$$ 6 -cycle systems

Non - Isomorphic 2 - Perfect 6 - Cycle Systems of Order 13

It is known that necessary and sufficient conditions for the existence of a 2-perfect 6-cycle system of order n are that n = 1 or 9 mod 12 and n > 9 (Lindner, Phelps and Rodger [2]). Hence the smallest possible order of such a system is 13. The existence of a 2-perfect 6-cycle system of order 13 is shown by example in [2]. The example is cyclic. It is obvious that for large n the construction o...

6 O ct 2 00 6 Semiclassical almost isometry

Let (M,ω, J) be a compact and connected polarized Hodge manifold, S an isodrastic leaf of half-weighted Bohr-Sommerfeld Lagrangian submanifolds. We study the relation between the Weinstein symplectic structure of S and the asymptotics of the the pull-back of the Fubini-Study form under the projectivization of the so-called BPU maps on S.

Metamorphosis of 2-fold 4-cycle systems into maximum packings of 2-fold 6-cycle systems

Perfect Graphs with No 2k 2 and No K 6

We prove that a 2K 2 minimal imperfect Berge graph (if any) contains a K 6 : A graph is perfect if the vertices of any induced subgraph H can be colored, in such a way that no two adjacent vertices receive the same color, with a number of colors (denoted by (H)) not exceeding the cardinality !(H) of a maximum clique of H. A graph is minimal imperfect if all its proper induced subgraphs are perf...

Completing some spectra for 2-perfect cycle systems

The determination of the spectrum for the decomposition of Kv into 2-perfect m-cycle systems is completed here for several small values of m. In particular, the cases m = 9, 12 and 16 are completed (except for three isolated cases). Other isolated 2-perfect m-cycle systems, some listed as unknown in a recent survey paper by Lindner and Rodger, have been found: namely, for Kv where (m,v) = (7,21...