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math.CO2022
On 1-skeleton of the polytope of pyramidal tours with step-backs
Andrei Nikolaev
Pyramidal tours with step-backs are Hamiltonian tours of a special kind: the salesperson starts in city 1, then visits some cities in ascending order, reaches city , and returns…
math.OC2022
Finding a second Hamiltonian decomposition of a 4-regular multigraph by integer linear programming
Andrei V. Nikolaev, Egor V. Klimov
A Hamiltonian decomposition of a regular graph is a partition of its edge set into Hamiltonian cycles. We consider the second Hamiltonian decomposition problem: for a 4-regular mul…