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|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|
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