Block-avoiding point sequencings of Mendelsohn triple systems

A cyclic ordering of the points in a Mendelsohn triple system of order v (or MTS(v)) is called a sequencing. A sequencing D is ℓ-good if there does not exist a triple (x, y, z) in the MTS(v) such that 1. the three points x, y, and z occur (cyclically) in that order in D; and 2. {x, y, z} is a subset of ℓ cyclically consecutive points of D. In this paper, we prove some upper bounds on ℓ for MTS(v) having ℓ-good sequencings and we prove that any MTS(v) with v ≥ 7 has a 3-good sequencing. We also determine the optimal sequencings of every MTS(v) with v ≤ 10