Block-avoiding point sequencings of Mendelsohn triple systems
Document Type
Article
Publication Date
5-2020
Department
Department of Mathematical Sciences
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.
Publication Title
Discrete Mathematics
Recommended Citation
Kreher, D. L.,
Stinson, D. R.,
&
Veitch, S.
(2020).
Block-avoiding point sequencings of Mendelsohn triple systems.
Discrete Mathematics,
343(5).
http://doi.org/10.1016/j.disc.2019.111799
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/1605
