##
Non-Separating Cycles Through Prescirbed Vertices in Plane Graphs

Non-Separating Cycles Through Prescirbed Vertices in Plane Graphs

dc.contributor.advisor | Ye, Dong | |

dc.contributor.author | Moser, Jacob | |

dc.contributor.committeemember | Stephens, Chris | |

dc.contributor.committeemember | Zha, Xiaoya | |

dc.date.accessioned | 2024-04-24T22:02:31Z | |

dc.date.available | 2024-04-24T22:02:31Z | |

dc.date.issued | 2024 | |

dc.date.updated | 2024-04-24T22:02:31Z | |

dc.description.abstract | A graph G is k-connected if it has at least k + 1 vertices and remains connected after deleting k − 1 vertices of G. A plane graph is a graph G with an embedding on a plane R2 such that the interior of an edge contains no vertex and no point of any other edge. When G is a plane graph, we call the regions of R2\G the faces of G. A planar graph is a graph isomorphic to a plane graph. A plane triangulation is a plane graph in which each face is bounded by a 3-cycle. A graph G is k-linked if, for any given 2k vertices there are k disjoint paths joining each pair of them. For a given graph H, a graph G is H-linked if, for every injective map from the vertices of H to the vertices of G, G contains a subdivision of H. Let (K4 − e) be the graph obtained from K4 by removing one edge. A graph G is (K4 − e)-linked if, for every injective map from the vertices of K4 − e to the vertices of G, G contains a subdivision of K4 − e. A graph is said to be k-cyclable if given any set of k vertices there is a cycle that contains the k vertices. We say that a graph is k-ordered or Ck-linked if given any set of k vertices there is a cycle through the k vertices in any specified order. A graph is (K2 ∪ K3)-linked if for every set of two vertices and every set of three vertices there exists a path joining the two vertices and a cycle on the three vertices. Seymour and Thomassen’s 2-linkage theorem characterizes all graphs which have two disjoint paths connecting any given two pair of vertices. Goddard proved that every 4-connected maximal planar graph is 4-ordered. Ellingham, Plummer, and Yu proved that any 4-connected planar triangulation is (K4 − e)-linked. In this thesis we completely characterize the obstructions to (K2 ∪ K3)-linkage in 4-connected plane triangulations. From these obstructions we can see that no 4-connected nor 5-connected plane triangulation is (K2 ∪ K3)-linked. iii | |

dc.description.degree | M.S. | |

dc.identifier.uri | https://jewlscholar.mtsu.edu/handle/mtsu/7184 | |

dc.language.rfc3066 | en | |

dc.publisher | Middle Tennessee State University | |

dc.source.uri | http://dissertations.umi.com/mtsu:11839 | |

dc.subject | 4-connected | |

dc.subject | Cyclability | |

dc.subject | Cyclable | |

dc.subject | Linkage | |

dc.subject | Planarity | |

dc.subject | Triangulation | |

dc.subject | Mathematics | |

dc.thesis.degreelevel | masters | |

dc.title | Non-Separating Cycles Through Prescirbed Vertices in Plane Graphs |

##### Files

##### Original bundle

1 - 1 of 1

No Thumbnail Available

- Name:
- Moser_mtsu_0170N_11839.pdf
- Size:
- 269.73 KB
- Format:
- Adobe Portable Document Format
- Description:

##### License bundle

1 - 1 of 1

No Thumbnail Available

- Name:
- license.txt
- Size:
- 2.27 KB
- Format:
- Item-specific license agreed upon to submission
- Description: