Induced-matching avoidance conjecture for partial edge colorings of hypercubes

Let $Q_d$ be the $d$-dimensional hypercube, and let $\varphi$ be a partial $d$-edge coloring of $Q_d$. A color class is the set of edges receiving one fixed color, and an induced matching is a matching whose endpoints induce no additional edges of $Q_d$. A partial coloring is avoidable if some proper $d$-edge coloring of $Q_d$ assigns a different color to every precolored edge than the one prescribed by $\varphi$. Induced-matching avoidance conjecture. If $d\ba3$ and every color class of $\varphi$ is an induced matching, then $\varphi$ is avoidable. The paper proves this when $d$ is a multiple of $3$, while conjecturing the statement for every $d\ba1$; the supplied candidate is the stronger formulation with $d\ba3$.