Now showing items 1-4 of 4
Connected co-spectral graphs are not necessarily both Hamiltonian
(Australian Mathematical Society, 2005)
There are many examples of co-spectral graphs where one is connected while the other is not. A Hamiltonian cycle is a closed path that visits every vertex exactly once. Naturally, a graph needs to be connected to be ...
A non-standard branch and bound method for the Hamiltonian cycle problem
(Australian Mathematical Society, 2000)
In this note, we consider an embedding of a Hamiltonian cycle problem in a Markov decision process (MDP). We propose a branch and bound type method based on the frequency polytope resulting from this embedding. Among the ...
Hamiltonian cycles and singularly perturbed Markov chains
We consider the Hamiltonian cycle problem embedded in a singularly perturbed Markov decision process. We also consider a functional on the space of deterministic policies of the process that consist of the (1,1)-entry of ...
Refined MDP-based branch-and-fix algorithm for the Hamiltonian cycle problem
We consider the famous Hamiltonian cycle problem (HCP) embedded in a Markov decision process (MDP). More specifically, we consider the HCP as an optimisation problem over the space of occupation measures induced by the ...