Embedding extended Mendelsohn triple systems

Mendelsohn directed triple systems

We introduce a class of ordered triple systems which are both Mendelsohn triple systems and directed triple systems. We call these Mendelsohn directed triple systems (MDTS(v, λ)), characterise them, and prove that they exist if and only if λ(v−1) ≡ 0 (mod 3). This is the same spectrum as that of regular directed triple systems, of which they are a special case. We also prove that cyclic MDTS(v,...

Mendelsohn Triple Systems excluding Contiguous Units with Λ = 1 Mendelsohn Triple Systems excluding Contiguous Units with Λ = 1

We obtain a necessary and sufficient condition for the existence of Mendelsohn triple systems excluding contiguous units with λ = 1. Also, we obtain the spectrum for cyclic such systems.

On the Number of Disjoint Mendelsohn Triple Systems

Further results about large sets of disjoint Mendelsohn triple systems

Kang, Q. and Y. Chang, Further results about large sets of disjoint Mendelsohn triple systems, Discrete Mathematics 118 (I 993) 2633268. In this note, a construction of the large sets of pairwise disjoint Mendelsohn triple systems of order 72k + 6, where k > 1 and k F 1 or 2 (mod 3), is given. Let X be a set of v elements (v 2 3). A cyclic triple from X is a collection of three pairs (x, y), (y...

The spectrum of rotational directed triple systems and rotational Mendelsohn triple systems

Necessary and sufficient conditions for the existence of k-rotational directed triple systems and k-rotational Mendelsohn triple systems are derived.