Date of Award

2019

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Poimenidou, Eirini

Area of Concentration

Mathematics

Abstract

Finding non-trivial necessary and sufficient conditions for the Hamiltonicity of graphs has been a longstanding open problem in Graph Theory. In this paper we prove a necessary and sufficient condition for a graph to be Hamiltonian. Moreover, we draw on past research of line graphs to highlight a surprising connection between the path and cyclic structure of a graph and the trails of hypergraphs. Finally, we briefly highlight some directions of future research.

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