Determining triangulations and quadrangulations by boundary distances
Combinatorics
2023-09-13 v2 Discrete Mathematics
Abstract
We show that if a disc triangulation has all internal vertex degrees at least 6, then the full triangulation may be determined from the pairwise graph distance between boundary vertices. A similar result holds for quadrangulations with all internal degrees at least 4. This confirms a conjecture of Itai Benjamini. Both degree bounds are best possible, and correspond to local non-positive curvature. However, we show that a natural conjecture for a "mixed" version of the two results is not true.
Keywords
Cite
@article{arxiv.2111.13556,
title = {Determining triangulations and quadrangulations by boundary distances},
author = {John Haslegrave},
journal= {arXiv preprint arXiv:2111.13556},
year = {2023}
}
Comments
18 pages, 5 figures. Final version, to appear in Journal of Combinatorial Theory, series B