Local move connectedness of domino tilings with diagonal impurities

We study the perfect matchings in the dual of the square–octagon lattice graph, which can be considered as domino tilings with impurities in some sense. In particular, we show the local move connectedness, that is, if G is a vertex induced finite subgraph which is simply connected, then any perfect matching in G can be transformed into any other perfect matching in G by applying a sequence of local moves each of which involves only two edges.