The k-walks in 2K2-free graphs
After a review of Hamiltonicity of graphs and related concepts, we discuss several generalizations of Hamilton cycles: k-walks, k-trees, Hamilton-prisms and edge-dominating cycles, and investigate the relationship between them. In particular, we focus on the Jackson-Wormald conjecture and show that...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Theses and Dissertations |
| Language: | English |
| Published: |
2016
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/10356/66352 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | After a review of Hamiltonicity of graphs and related concepts, we discuss several generalizations of Hamilton cycles: k-walks, k-trees, Hamilton-prisms and edge-dominating cycles, and investigate the relationship between them. In particular, we focus on the Jackson-Wormald conjecture and show that it holds for a graph with an edge-dominating cycle. The latter gives us our central result: an efficient algorithmic proof of Jackson-Wormald conjecture for 2K_2-free graphs. Another main result is that each (1+\epsilon) -tough 2K_2-free graph is prism-Hamiltonian. Generally, being prism-Hamiltonian is a stronger property than admitting k-walks for all k\ge2, but weaker than being traceable. Finally, we present several results on the existence of 2-walks under the 1-toughness assumption for some other graphs, and pose conjectures for further research. |
|---|