Penrose P2 Tilings: A Study of Fully Leafed Induced Subtrees
Combinatorics
2026-03-12 v1
Abstract
We present new results about fully leafed induced subtrees in Penrose P2 tilings. We first determine the graph structure of these subtrees and show that they are caterpillars, up to an appendix of at most six tiles. We then study bi-infinite fully leafed induced caterpillars in P2 tilings and their geometric properties. In particular, we refute the conjecture proposed by C. Porrier, A. Goupil and A. Blondin Mass\'e that there is a unique bi-infinite fully leafed caterpillar in Penrose P2 tilings.
Keywords
Cite
@article{arxiv.2603.10172,
title = {Penrose P2 Tilings: A Study of Fully Leafed Induced Subtrees},
author = {Mathieu Cloutier and Alain Goupil and Alexandre Blondin Massé},
journal= {arXiv preprint arXiv:2603.10172},
year = {2026}
}
Comments
Conference paper submitted to GASCom 2026. Full version: arXiv:2602.13798