### 抄録

Izmestiev, Klee and Novik proved that any two balanced triangulations of a closed surface F^{2} can be transformed into each other by a sequence of six operations called basic cross flips. Recently Murai and Suzuki proved that among these six operations only two operations are almost sufficient in the sense that, with for finitely many exceptions, any two balanced triangulations of a closed surface F^{2} can be transformed into each other by these two operations. We investigate such finitely many exceptions, called exceptional balanced triangulations, and obtain the list of exceptional balanced triangulations of closed surfaces with low genera. Furthermore, we discuss the subsets O of the six operations satisfying the property that any two balanced triangulations of the same closed surface can be connected through a sequence of operations from O.

元の言語 | English |
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ジャーナル | Graphs and Combinatorics |

DOI | |

出版物ステータス | Accepted/In press - 2019 1 1 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### これを引用

*Graphs and Combinatorics*. https://doi.org/10.1007/s00373-018-2001-x

**Exceptional Balanced Triangulations on Surfaces.** / Klee, Steven; Murai, Satoshi; Suzuki, Yusuke.

研究成果: Article

*Graphs and Combinatorics*. https://doi.org/10.1007/s00373-018-2001-x

}

TY - JOUR

T1 - Exceptional Balanced Triangulations on Surfaces

AU - Klee, Steven

AU - Murai, Satoshi

AU - Suzuki, Yusuke

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Izmestiev, Klee and Novik proved that any two balanced triangulations of a closed surface F2 can be transformed into each other by a sequence of six operations called basic cross flips. Recently Murai and Suzuki proved that among these six operations only two operations are almost sufficient in the sense that, with for finitely many exceptions, any two balanced triangulations of a closed surface F2 can be transformed into each other by these two operations. We investigate such finitely many exceptions, called exceptional balanced triangulations, and obtain the list of exceptional balanced triangulations of closed surfaces with low genera. Furthermore, we discuss the subsets O of the six operations satisfying the property that any two balanced triangulations of the same closed surface can be connected through a sequence of operations from O.

AB - Izmestiev, Klee and Novik proved that any two balanced triangulations of a closed surface F2 can be transformed into each other by a sequence of six operations called basic cross flips. Recently Murai and Suzuki proved that among these six operations only two operations are almost sufficient in the sense that, with for finitely many exceptions, any two balanced triangulations of a closed surface F2 can be transformed into each other by these two operations. We investigate such finitely many exceptions, called exceptional balanced triangulations, and obtain the list of exceptional balanced triangulations of closed surfaces with low genera. Furthermore, we discuss the subsets O of the six operations satisfying the property that any two balanced triangulations of the same closed surface can be connected through a sequence of operations from O.

KW - Balanced triangulation

KW - Closed surface

KW - Local transformation

UR - http://www.scopus.com/inward/record.url?scp=85059835322&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059835322&partnerID=8YFLogxK

U2 - 10.1007/s00373-018-2001-x

DO - 10.1007/s00373-018-2001-x

M3 - Article

AN - SCOPUS:85059835322

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

ER -