On the Computation and Chromatic Number of Colored Domino Tilings
نویسندگان
چکیده
A colored domino is a rotatable 2× 1 rectangle that is partitioned into two unit squares, which are called faces, each of which is assigned a color. In a colored domino tiling of an orthogonal polygon P , a set of dominoes completely covers P such that no dominoes overlap and so that adjacent faces have the same color. We provide tight bounds on the number of colors required to tile simple and non-simple orthogonal polygons. We also present an algorithm for computing a colored domino tiling of a simple orthogonal polygon.
منابع مشابه
A Variational Principle for Domino Tilings
1.1. Description of results. A domino is a 1×2 (or 2×1) rectangle, and a tiling of a region by dominos is a way of covering that region with dominos so that there are no gaps or overlaps. In 1961, Kasteleyn [Ka1] found a formula for the number of domino tilings of an m × n rectangle (with mn even), as shown in Figure 1 for m = n = 68. Temperley and Fisher [TF] used a different method and arrive...
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