Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/66352
 Title: The k-walks in 2K2-free graphs Authors: Gao, Mou Keywords: DRNTU::Science Issue Date: 2016 Abstract: 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. URI: http://hdl.handle.net/10356/66352 Fulltext Permission: restricted Fulltext Availability: With Fulltext Appears in Collections: SPMS Theses

###### Files in This Item:
File Description SizeFormat
thesis Gao Mou.pdf
Restricted Access