A characterization of Hamiltonian prisms

Abstract

A characterization is established for a graph G to have a Hamilton cycle in G x K2, the prism over G. Moreover, it is shown that every 3-connected graph has a 2-connected spanning bipartite subgraph. Using this result, the existence of a Hamilton cycle in the prism over every 3-connected cubic graph is established. Further, the existence of a Hamilton cycle in the prism over a cubic 2-connected graph is also discussed. Earlier results in this direction are shown to be particular cases of the results obtained here. 0 1993 John Wiley & Sons, Inc.

Traversing every edge in each direction once, but not at once: Cubic (polyhedral) graphs

“…In some instances, the Hamiltonicity of G guarantees that G has more than one Hamiltonian cycle [21]. There were studied in detail Hamiltonian ladders (defined by the Cartesian product G × K 2 of G and K 2 ) [22], which are a generalization of graphs of prisms.…”

The Prism Over the Middle-levels Graph is Hamiltonian

“…By [9] (see also [1]), any 3-connected cubic graph has a hamiltonian prism. Thus, the assertion follows from Theorem 8.…”

“…For a nice survey of results on k-walks, k-trees and related topics, we refer the reader to Ellingham [4]. The prism over a graph G is the Cartesian product G2K 2 of G with the complete graph K 2 [1,7,9]. Thus, it consists of two copies of G and a 1-factor joining the corresponding vertices.…”

Hamilton cycles in prisms

“…Fleischner [12] found a proof avoiding the use of the Four Color Theorem. Eventually, Paulraja [21] showed that planarity is inessential here.…”