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 ...
We develop a new, random walk-based, algorithm for the Hamiltonian cycle problem. The random walk is on pairs of extreme points of two suitably constructed polytopes. The latter are derived from ...
As mathematical abstractions go, graphs are among the simplest. Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph is. And yet they are incredibly powerful. They ...
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