Hamilton Paths in Generalized Petersen Graphs

Abstract

This thesis puts forward the conjecture that for <i>n</i> > 3<i>k</i> with <i>k</i> > 2, the generalized Petersen graph, <i>GP</i>(<i>n,k</i>) is Hamilton-laceable if <i>n</i> is even and <i>k</i> is odd, and it is Hamilton-connected otherwise. We take the first step in the proof of this conjecture by proving the case <i>n</i> = 3<i>k</i> + 1 and <i>k</i> greater than or equal to 1. We do this mainly by means of an induction which takes us from <i>GP</i>(3<i>k</i> + 1, <i>k</i>) to <i>GP</i>(3(<i>k</i> + 2) + 1, <i>k</i> + 2). The induction takes the form of mapping a Hamilton path in the smaller graph piecewise to the larger graph an inserting subpaths we call <i>rotors</i> to obtain a Hamilton path in the larger graph.