dc.contributor.authorGao, Mou
dc.description.abstractAfter 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.en_US
dc.format.extent109 p.en_US
dc.titleThe k-walks in 2K2-free graphsen_US
dc.contributor.supervisorDmitrii V Pasechniken_US
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.description.degree​Doctor of Philosophy (SPMS)en_US

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