Balanced subdivisions and flips on surfaces
Combinatorics
2017-01-30 v1
Abstract
In this paper, we show that two balanced triangulations of a closed surface are not necessary connected by a sequence of balanced stellar subdivisions and welds. This answers a question posed by Izmestiev, Klee and Novik. We also show that two balanced triangulations of a closed surface are connected by a sequence of three local operations, which we call the pentagon contraction, the balanced edge subdivision and the balanced edge weld. In addition, we prove that two balanced triangulations of the 2-sphere are connected by a sequence of pentagon contractions and their inverses if none of them are octahedral spheres.
Cite
@article{arxiv.1701.08060,
title = {Balanced subdivisions and flips on surfaces},
author = {Satoshi Murai and Yusuke Suzuki},
journal= {arXiv preprint arXiv:1701.08060},
year = {2017}
}
Comments
12 pages