Monotone labelings in polygonal tilings

Labeling the vertices of a finite sequence of polygonal tilings with fewest monotonicity violations enables us to represent the tilings by merely specifying sets of vertices – the sequence of their appearance results from the labels. Eventually, this allows a lossless data compression for the sequence of tilings. The existence and computation of suitable labelings is derived from matching and graph colorings which induce an order on the tilings. This order is series-parallel on each individual tiling.