# Connectivity Properties of the Flip Graph After Forbidding Triangulation Edges

dc.contributor.author | Bigdeli, Reza | |

dc.date.accessioned | 2022-09-23T20:22:16Z | |

dc.date.available | 2022-09-23T20:22:16Z | |

dc.date.issued | 2022-09-23 | |

dc.date.submitted | 2022-09-14 | |

dc.description.abstract | The flip graph for a set $P$ of points in the plane has a vertex for every triangulation of $P$, and an edge when two triangulations differ by one flip that replaces one triangulation edge by another. The flip graph is known to have some connectivity properties: (1) the flip graph is connected; (2) connectivity still holds when restricted to triangulations containing some constrained edges between the points; (3) for $P$ in general position of size $n$, the flip graph is $\lceil \frac{n}{2} -2 \rceil$-connected, a recent result of Wagner and Welzl (SODA 2020). We introduce the study of connectivity properties of the flip graph when some edges between points are forbidden. An edge $e$ between two points is a flip cut edge if eliminating triangulations containing $e$ results in a disconnected flip graph. More generally, a set $X$ of edges between points of $P$ is a flip cut set if eliminating all triangulations that contain edges of $X$ results in a disconnected flip graph. The flip cut number of $P$ is the minimum size of a flip cut set. We give a characterization of flip cut edges that leads to an $O(n \log n)$ time algorithm to test if an edge is a flip cut edge and, with that as preprocessing, an $O(n)$ time algorithm to test if two triangulations are in the same connected component of the flip graph. For a set of $n$ points in convex position (whose flip graph is the 1-skeleton of the associahedron) we prove that the flip cut number is $n-3$. | en |

dc.identifier.uri | http://hdl.handle.net/10012/18787 | |

dc.language.iso | en | en |

dc.pending | false | |

dc.publisher | University of Waterloo | en |

dc.subject | computation geometry | en |

dc.subject | graph connectivity | en |

dc.subject | combinatorial optimization | en |

dc.title | Connectivity Properties of the Flip Graph After Forbidding Triangulation Edges | en |

dc.type | Master Thesis | en |

uws-etd.degree | Master of Mathematics | en |

uws-etd.degree.department | David R. Cheriton School of Computer Science | en |

uws-etd.degree.discipline | Computer Science | en |

uws-etd.degree.grantor | University of Waterloo | en |

uws-etd.embargo.terms | 0 | en |

uws.contributor.advisor | Lubiw, Anna | |

uws.contributor.affiliation1 | Faculty of Mathematics | en |

uws.peerReviewStatus | Unreviewed | en |

uws.published.city | Waterloo | en |

uws.published.country | Canada | en |

uws.published.province | Ontario | en |

uws.scholarLevel | Graduate | en |

uws.typeOfResource | Text | en |