Block-avoiding point sequencings of Mendelsohn triple systems

Abstract 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 .