Hamilton paths in generalized Petersen graphs

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