Balanced subdivisions and flips on surfaces

Satoshi Murai, Yusuke Suzuki

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we show that two balanced triangulations of a closed surface are not necessarily 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 the octahedral sphere.

Original languageEnglish
Pages (from-to)939-951
Number of pages13
JournalProceedings of the American Mathematical Society
Volume146
Issue number3
DOIs
Publication statusPublished - 2018 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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