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arXiv · 2605.24289

An Exact Continuous Conductance Formulation of the Hamiltonian Path Problem

A. Sadovsky
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Abstract

The Hamiltonian Path Problem is formulated as a continuous minimization problem on conductances assigned to an Ohmic network associated with the given graph. The objective function is a sum of two penalty terms that collectively enforce a set of conditions sufficient for a subgraph of the original graph to be a Hamiltonian path. The objective function is nonconvex. The main result (Theorem 1) shows that, provided the graph has a Hamiltonian path from $h^{start}$ to $h^{end}$, a conductance configuration is a global minimizer of the objective if and only if it corresponds to a Hamiltonian path.

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A. Sadovsky. 2026-05-22. An Exact Continuous Conductance Formulation of the Hamiltonian Path Problem. https://arxiv.org/abs/2605.24289

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