First, we show that the determinant of a given matrix can be expanded by its principal minors together with a set of arbitrary parameters. The enumeration of Hamiltonian cycles and paths in a graph is ...

The modern information society is enabled by photonic fiber networks characterized by huge coverage and great complexity and ranging in size from transcontinental submarine telecommunication cables to ...

It is commonly believed that vertex-transitive graphs (and in particular Cayley graphs) tend to contain hamilton cycles. The only known connected vertex-transitive graphs without hamilton cycles are K ...

In algorithms, as in life, negativity can be a drag. Consider the problem of finding the shortest path between two points on a graph — a network of nodes connected by links, or edges. Often, these ...