<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>As a sequel of a previous paper by the authors, we present here a generating theorem for the family of triangulations of an arbitrary punctured surface with vertex degree ≥ 4. The method is based on a series of reversible operations termed reductions which lead to a minimal set of triangulations in such a way that all intermediate triangulations throughout the reduction process remain within the family. Besides contractible edges and octahedra, the reduction operations act on two new configurations near the surface boundary named quasi-octahedra and <italic>N</italic>-components. It is also observed that another configuration called <italic>M</italic>-component remains unaltered under any sequence of reduction operations. We show that one gets rid of <italic>M</italic>-components by flipping appropriate edges.</p>
</abstract>

As a sequel of a previous paper by the authors, we present here a generating theorem for the family of triangulations of an arbitrary punctured surface with vertex degree ≥ 4. The method is based on a series of reversible operations termed reductions which lead to a minimal set of triangulations in such a way that all intermediate triangulations throughout the reduction process remain within the family. Besides contractible edges and octahedra, the reduction operations act on two new configurations near the surface boundary named quasi-octahedra and N-components. It is also observed that another configuration called M-component remains unaltered under any sequence of reduction operations. We show that one gets rid of M-components by flipping appropriate edges.

Generating punctured surface triangulations with degree at least 4

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Generating punctured surface triangulations with degree at least 4"}

As a sequel of a previous paper by the authors, we present here a generating theorem for the family of triangulations of an arbitrary punctured surface with...

Generating punctured surface triangulations with degree at least 4

Published Online: Mar 12, 2022

Page range: 129 - 151

Received: Apr 22, 2021

Accepted: Jul 25, 2021

DOI: https://doi.org/10.2478/auom-2022-0008

Keywords
Punctured surface, irreducible triangulation, edge contraction, vertex splitting, removal/addition of octahedra, generating theorem

© 2022 María-José Chávez et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Generating punctured surface triangulations with degree at least 4

Published Online: Mar 12, 2022

Page range: 129 - 151

Received: Apr 22, 2021

Accepted: Jul 25, 2021

DOI: https://doi.org/10.2478/auom-2022-0008

KeywordsPunctured surface, irreducible triangulation, edge contraction, vertex splitting, removal/addition of octahedra, generating theorem

© 2022 María-José Chávez et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Punctured surface, irreducible triangulation, edge contraction, vertex splitting, removal/addition of octahedra, generating theorem