Semester
Summer
Date of Graduation
2005
Document Type
Dissertation
Degree Type
PhD
College
Eberly College of Arts and Sciences
Department
Mathematics
Abstract
The research of my dissertation is motivated by the conjecture of Thomassen that every 4-connected line graph is hamiltonian and by the conjecture of Tutte that every 4-edge-connected graph has a no-where-zero 3-flow. Towards the hamiltonian line graph problem, we proved that every 3-connected N2-locally connected claw-free graph is hamiltonian, which was conjectured by Ryjacek in 1990; that every 4-connected line graph of an almost claw free graph is hamiltonian connected, and that every triangularly connected claw-free graph G with |E( G)| ≥ 3 is vertex pancyclic. Towards the second conjecture, we proved that every line graph of a 4-edge-connected graph is Z 3-connected.
Recommended Citation
Shao, Yehong, "Claw -free graphs and line graphs" (2005). Graduate Theses, Dissertations, and Problem Reports (ETD). 2251.
https://researchrepository.wvu.edu/etd/2251