Karen Holbert

Date of Defense

Spring 4-21-1979

Department

Mathematics

Keywords

graph theory, eulerian trail, euler walk, eulerian cycle, euler tour, eulerian circuit

Abstract

This paper considers eulerian and hamiltonian graphs from a comparison point of view. The origins of both classes of graphs are compared by means of a brief historical sketch. The use of hamiltonian and eulerian graphs as models of transportation problems is discussed. For example, it is mentioned that eulerian graphs can sometimes be used in scheduling routes for postmen and policemen, while hamiltonian graphs may be used to decide routes for traveling salesmen. In the case of eulerian graphs, a characterization and also an algorithm for determining an eulerian circuit in an eulerian graph are presented. Hamiltonian graphs are studied next, and some sufficient conditions for a graph to be hamiltonian are given. The main emphasis of this paper is on the algorithms presented and the lack of a useful characterization of hamiltonian graphs from an efficient algorithmic viewpoint.

Access Setting

Honors Thesis-Campus Only

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