论文标题
5%的飞机可以正确5和6色?
What percent of the plane can be properly 5- and 6-colored?
论文作者
论文摘要
我们提出的占地99.985698%的欧几里得平面具有六种颜色,使前面未发现平面的记录减少了约12.8%。我们还展示了超过95.99%的瓷砖,上面有五种颜色。因此,表明,在平面中最多可在6992和24处的任何单位距离图分别进行6色和5色。
We present a tiling of more than 99.985698% of the Euclidean plane with six colors, reducing the previous record for uncovered fraction of the plane by about 12.8%. We also present a tiling of more than 95.99% of the plane with five colors. It is thus shown that any unit-distance graph of order at most 6992 and 24 in the plane can be properly 6-colored and 5-colored, respectively.