I would like to know if there are existing results on the following objects:
spanning trees of a grid graph, with no corridor
where a corridor is a vertex having exactly two neighbors, on opposite sides.
Here is a picture of a spanning tree with corridors in red:
I would be interested in counting and random generation. Is there some variant of the classical methods for spanning trees that would work for them?
I am motivated by some representation-theoretic setting where a corridor allows to factorise the situation.
The similar problem for planar binary trees is much simpler (see Oeis sequence A5554).