Exceptional Balanced Triangulations on Surfaces

Steven Klee, Satoshi Murai, Yusuke Suzuki

    Research output: Contribution to journal › Article

    Abstract

    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.

    Original languageEnglish
    JournalGraphs and Combinatorics
    DOIs
    Publication statusAccepted/In press - 2019 Jan 1

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    Triangulation
    Closed
    Exception
    Flip
    Genus
    Sufficient
    Subset

    Keywords

    • Balanced triangulation
    • Closed surface
    • Local transformation

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Discrete Mathematics and Combinatorics

    Cite this

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

    In: Graphs and Combinatorics, 01.01.2019.

    Research output: Contribution to journal › Article

    Klee, S, Murai, S & Suzuki, Y 2019, 'Exceptional Balanced Triangulations on Surfaces' Graphs and Combinatorics. https://doi.org/10.1007/s00373-018-2001-x
    Klee S, Murai S, Suzuki Y. Exceptional Balanced Triangulations on Surfaces. Graphs and Combinatorics. 2019 Jan 1. https://doi.org/10.1007/s00373-018-2001-x
    Klee, Steven ; Murai, Satoshi ; Suzuki, Yusuke. / Exceptional Balanced Triangulations on Surfaces. In: Graphs and Combinatorics. 2019.
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