Domino tilings on planar regions (Q1924219)

\textit{J. H. Conway} and \textit{J. C. Lagarias} [J. Comb. Theory, Ser. A 53, No. 2, 183-208 (1990; Zbl 0741.05019)] and \textit{W. P. Thurston} [Am. Math. Mon. 95, No. 8, 757-773 (1990; Zbl 0714.52007)], using combinatorial group theory, give necessary and sufficient conditions for a simply-connected region of a checkerboard to be tiled by dominoes. The paper under review considers domino tilings of planar checkerboard-like regions, a generalization that properly includes multiply-connected subsets of the checkerboard. Ito gives necessary and sufficient conditions for such a region to be tiled by dominoes in terms of null-homologous closed edge paths of the region.