English

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.

Keywords

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

R2 v1 2026-06-22T18:02:28.451Z