Class PalmerHamiltonianCycle<V,​E>

  • Type Parameters:
    V - the graph vertex type
    E - the graph edge type
    All Implemented Interfaces:

    public class PalmerHamiltonianCycle<V,​E>
    extends Object
    implements HamiltonianCycleAlgorithm<V,​E>
    Palmer's algorithm for computing Hamiltonian cycles in graphs that meet Ore's condition. Ore gave a sufficient condition for a graph to be Hamiltonian, essentially stating that a graph with sufficiently many edges must contain a Hamilton cycle. Specifically, Ore's theorem considers the sum of the degrees of pairs of non-adjacent vertices: if every such pair has a sum that at least equals the total number of vertices in the graph, then the graph is Hamiltonian.

    A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node exactly once (Skiena 1990, p. 196).

    This is an implementation of the algorithm described by E. M. Palmer in his paper. The algorithm takes a simple graph that meets Ore's condition (see GraphTests.hasOreProperty(Graph)) and returns a Hamiltonian cycle. The algorithm runs in $O(|V|^2)$ time and uses $O(|V|)$ space.

    The original algorithm is described in: Palmer, E. M. (1997), "The hidden algorithm of Ore's theorem on Hamiltonian cycles", Computers & Mathematics with Applications, 34 (11): 113–119, doi:10.1016/S0898-1221(97)00225-3 See wikipedia for a short description of Ore's theorem and Palmer's algorithm.

    Alexandru Valeanu