On the Chromatic Number of Subsets of the Euclidean Plane
On the Chromatic Number of Subsets of the Euclidean Plane
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DOI：
10.1007/s00373-012-1249-9
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发表时间：
2012-11
影响因子：
0.7
通讯作者：
M. Axenovich;Jihyeok Choi;M. Lastrina;Tracy McKay;J. Smith;B. Stanton
中科院分区：
文献类型：
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作者：
M. Axenovich;Jihyeok Choi;M. Lastrina;Tracy McKay;J. Smith;B. Stanton
实平面的子集的色数是分配给该集合的元素的颜色的最小数目，使得在距离1处没有两个点接收相同的颜色。已知平面的色数至少为4，至多为7。在这篇注记中，我们确定了平面的几类子集的色数的界，如有理平面的扩张、凸位点集、无限条、平行线等。
The chromatic number of a subset of the real plane is the smallest number of colors assigned to the elements of that set such that no two points at distance 1 receive the same color. It is known that the chromatic number of the plane is at least 4 and at most 7. In this note, we determine the bounds on the chromatic number for several classes of subsets of the plane such as extensions of the rational plane, sets in convex position, infinite strips, and parallel lines.