= Solution
Two dual <faces of a plane graph> share an <edge> exactly when their corresponding original <vertices> are adjacent. Their face-adjacency <graph> is therefore the original <tree>, which is a nontrivial <bipartite graph>. Colour the face for $r$ with one colour and alternate along the original <tree>. This gives a proper <face colouring> with two colours, and at least two are needed because there is an <edge> separating distinct faces. Hence the minimum is
$$
\boxed{2.}
$$
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