Skolem sequences: Generalizations and applications

Abstract

<p>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.</p>