Decidability Problems of Triangle Edge-coloring

• Main Authors: Chen, Hung-Shiun, 陳泓勳
• Other Authors: Lin, Song-Sun
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/60033521582725706434

碩士 === 國立交通大學 === 應用數學系所 === 98 === This investigation is about tiling the whole plane with upper triangles and lower triangles which have colors on edges. Upper and lower triangles can be placed side by side if each of the intersections has the same color. In this paper, we consider upper and lower triangle with two and three colors on edges. The problem we studied is that: any set of triangle that can fill with the whole plane whether it can cover the whole plane periodically. We use an algorithm to do the problem and get the result by computers. Finally, the main result of this paper is that the whole plane can be tiling by triangle with two and three colors if and only if the whole plane is covered by the local pattern periodically.