Circuits, Perfect Matchings and Paths in Graphs

We primarily consider the problem of finding a family of circuits to cover a bidgeless graph (mainly on cubic graph) with respect to a given weight function defined on the edge set. The first chapter of this thesis is going to cover all basic concepts and notations will be used and a survey of this topic.;In Chapter two, we shall pay our attention to the Strong Circuit Double Cover Conjecture (SCDC Conjecture). This conjecture was verified for some graphs with special structure. As the complement of two factor in cubic graph, the Berge-Fulkersen Conjecture was introduced right after SCDC Conjecture. In Chapter three, we shall present a series of conjectures related to perfect matching covering and point out their relationship.;In last chapter, we shall introduce the saturation number, in contrast to extremal number (or known as Turan Number), and describe the edge spectrum of saturation number for small paths, where the spectrum was consisted of all possible integers between saturation number and Turan number.

Name thesis:degree_name

PhD

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2013

Author dc:creator

• Tang, Wenliang

Contributors dc:contributor

• Cun-Quan Zhang
• Mark Culp
• John Goldwasser
• Hong-Jian Lai
• Jerzy Wojciechowski

• Mathematics
• Theoretical mathematics
• Applied mathematics

Identifier

https://researchrepository.wvu.edu/etd/386

OAI identifier oai:identifier

oai:researchrepository.wvu.edu:etd-1389