Outlet Title

Discrete Mathematics

Document Type

Article

Publication Date

2026

Abstract

The cycle structure of Steiner triple systems (STS) has been well studied with regard to uniform STS and cycle switching. Of particular interest among uniform STS are perfect STS, in which every cycle graph consists of a single cycle. In this paper, we initiate the study of antiperfect STS, in which every cycle graph consists of a union of at least two cycles. We prove that an antiperfect STS(n) exists for all admissible n ≥ 15 and provide a complete listing of all antiperfect STS(n) for n ≤ 19 and all antiperfect STS(21) with a non-trivial automorphism. Furthermore, it is shown that antiperfect Steiner triple systems can be used to address an open question of Häggkvist on 1-factorizations of Kn,n in which the length of cycles formed by the union of any two 1-factors is as small as possible. The paper closes with a number of conjectures and open questions related to antiperfect STS.

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