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Author

Nabil Shalaby

Date of Award

8-1991

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Supervisor

Alexander Rosa

Abstract

In this thesis the necessary conditions for the existence of near-, hooked near-, and indecomposable Skolem sequences are found and shown to be sufficient. We show also the existence of disjoint Skolem, disjoint hooked Skolem and disjoint near-Skolem sequences. Disjoint Skolem sequences are then applied to the existence problems for disjoint cyclic Steiner and Mendelsohn triple systems. We also consider Skolem labellings of graphs: we prove that every graph with v vertices can be embedded as an induced subgraph in a Skolem labelled graph on O(v³) vertices, and show that all paths, cycles and n-windmills can be Skolem labelled or minimum hooked Skolem labelled.

Included in

Mathematics Commons

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