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Δ-Y Moves and Partial Steiner Systems
Abstract
We study graph systems generated by Δ-Y and Y-Δ moves and prove that, for initial graphs of minimum degree at least $7$, Δ-Y moves alone generate every reachable graph. As a consequence, for n≥ 8, the Δ-Y system generated from the complete graph of n vertices is canonically isomorphic as graded directed graphs to the space of partial Steiner systems on n points.
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BibTeX
@misc{zhou2026moves,
title = {{$Δ$-Y Moves and Partial Steiner Systems}},
author = {Zhichen Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08963},
eprint = {2609.08963},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08963},
}
RIS
TY - UNPB
TI - Δ-Y Moves and Partial Steiner Systems
AU - Zhichen Zhou
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08963
UR - https://arxiv.org/abs/2609.08963
AB - We study graph systems generated by Δ-Y and Y-Δ moves and prove that, for initial graphs of minimum degree at least $7$, Δ-Y moves alone generate every reachable graph. As a consequence, for n≥ 8, the Δ-Y system generated from the complete graph of n vertices is canonically isomorphic as graded directed graphs to the space of partial Steiner systems on n points.
ER -