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A distribution is faithful to a Directed acyclic graph $G$ when every conditional independence in the distribution is implied by D-separation in $G$. Together with the graphical Markov property, faithfulness makes conditional independence equivalent to D-separation and rules out independences caused only by exact parameter cancellation.

For a distribution faithful to a Directed acyclic graph, the smallest Markov blanket of a vertex consists of

Conditioning on this set blocks every path from the vertex to all remaining vertices. Each listed neighbor is necessary under faithfulness of a directed acyclic graph: omitting a parent or child leaves its direct edge active, while omitting a child's other parent leaves the collider path through that conditioned child active. Faithfulness rules out accidental cancellations that could otherwise make a smaller blanket sufficient.