Tiling by hyperbolic dominoes (Q294081)

The paper under review deals with tilings of two-dimensional Riemannian spaces of constant curvature. The authors provide an original combinatorial proof of a criterion which allows to decide whether a given domain, a bicolored board, in \(\mathbb E^2\) (\(\mathbb S^2\), \(\mathbb H^2\)) may be tiled by dominoes. The proof uses ideas developed by \textit{W. P. Thurston} [Am. Math. Mon. 97, No. 8, 757--773 (1990; Zbl 0714.52007)] for the Euclidean tilings; the authors adapt and generalize Thurston's methods to the spherical and hyperbolic cases.