Fully Leafed Induced Subtrees in Penrose P2 Tilings
Combinatorics
2026-02-17 v1
Abstract
In a recent article by C. Porrier, A. Blondin Mass\'e and A. Goupil, a first bi-infinite fully leafed induced subcaterpillar of Penrose P2 tilings is presented. In this paper, we formally construct this caterpillar for the first time. We then prove that every fully leafed induced subtree in Penrose P2 tilings is a caterpillar with at most one appendix of at most two internal tiles, and we characterize fully leafed induced subtrees that have the property of saturation. We also refute the conjecture that there is a unique bi-infinite fully leafed induced subcaterpillar by constructing a new one. Finally, we present progress on the construction of all bi-infinite fully leafed induced subcaterpillars in Penrose P2 tilings.
Cite
@article{arxiv.2602.13798,
title = {Fully Leafed Induced Subtrees in Penrose P2 Tilings},
author = {Mathieu Cloutier and Alain Goupil and Alexandre Blondin Massé},
journal= {arXiv preprint arXiv:2602.13798},
year = {2026}
}
Comments
42 pages, 111 figures