Download PDFOpen PDF in browserColoring Unit-Distance Strips using SAT17 pages•Published: May 27, 2020AbstractSatisfiability (SAT) solving has become an important technology in computer-aided mathematics with various successes in number and graph theory. In this paper we apply SAT solvers to color infinitely long strips in the plane with a given height and number of colors. The coloring is constrained as follows: two points that are exactly unit distance apart must be colored differently. To finitize the problem, we tile the strips and all points on a tile have the same color. We evaluated our approach using two different tile shapes: squares and hexagons. The visualization of bounded height strips using 3 to 6 colors reveal patterns that are similar to the best known lower bounds for infinite strips. Our method can be a useful tool for mathematicians to search for patterns that can be generalized to infinite strips and allowed us to increase the lower bound for the strip height with 5 colors to an improved height of 1.700084.Keyphrases: chromatic number of the plane, graph coloring, sat solving In: Elvira Albert and Laura Kovacs (editors). LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 73, pages 373-389.
|