Existence and construction of Hamiltonian paths and cycles on conforming tetrahedral meshes
Hui Liu, Linbo Zhang · International Journal of Computer Mathematics · 2011
This paper addresses the existence and construction of Hamiltonian paths and Hamiltonian cycles on conforming tetrahedral meshes. The paths and cycles are constrained to pass from one tetrahedron to the next one through a vertex. For conforming tetrahedral meshes, under certain conditions which are normally satisfied in finite-element computations, we show that there exists a through-vertex Hamiltonian path between any two tetrahedra. The proof is constructive from which an efficient algorithm for computing Hamiltonian paths and cycles can be directly derived.