The polynomial-size DFJ relaxation conjecture for cubic graphs

Let $amma$ be a cubic graph. Let $Mathcal{P}_b$ be the feasible region defined by constraints

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, and let $Mathcal{P}_c$ be the feasible region defined by the degree, subtour, symmetry, upper-bound, and nonnegativity constraints

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, where $S$ ranges over proper subsets of the vertices of $amma$. Polynomial-size DFJ relaxation conjecture. The constraints

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form a polynomial-size set equivalent to the exponential-size set

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; equivalently, $\mathcal{P}_b=\mathcal{P}_c$. If true, this would provide a polynomial-size description of the DFJ feasible region for every cubic graph. The claim is motivated only by computational comparisons in the source, which reports that the two formulations identified exactly the same tested non-Hamiltonian graphs; no resolution is given.