We study Hamiltonian unfolding—cutting a convex polyhedron along a Hamiltonian path of edges to unfold it without overlap—of two classes of polyhedra. Such unfoldings could be implemented by a single zipper, so they are also known as zipper edge unfoldings. First we consider domes, which are simple convex polyhedra. We find a family of domes whose graphs are Hamiltonian, yet any Hamiltonian unf...

We introduce and study a d-dimensional generalization of graph Hamiltonian cycles. These are the cycles in Knd (the complete simplicial d-complex over vertex set size n). d-cycles simple rank, or, equivalently, 1+(n−1d). The discussion is restricted to fields F2 Q. For d=2, we characterize n's for which 2-cycles exist. d=3 it shown that 3-cycles exist infinitely many n's. In general, there alwa...

Hypercubes are famous interconnection networks. The shuffle cubes are proposed as its variation with lower diameter. In this paper, we concentrate on the fault tolerant hamiltonicity and hamiltonian connectivity of the shuffle cube. We say that a graph G is f-hamiltonian if there is a hamiltonian cycle in G − F and is f-hamiltonian connected if there is a hamiltonian path between any two vertic...

In this paper, we discuss hamiltonian problems for reducible Powgraphs. The main result is finding, in linear time, the unique hamiltonian cycle, if it exists. In order to obtain this result, two other related problems are solved: finding the hamiltonian path starting at the source vertex and finding the hamiltonian cycle given the hamiltonian path.

The Hamiltonian cycle problem is to decide whether a given graph has a Hamiltonian cycle. Bertossi and Bonuccelli (1986, Information Processing Letters, 23, 195200) proved that the Hamiltonian Cycle Problem is NP-Complete even for undirected path graphs and left the Hamiltonian cycle problem open for directed path graphs. Narasimhan (1989, Information Processing Letters, 32, 167-170) proved tha...