Almost Empty Monochromatic Quadrilaterals in Planar Point Sets
- 作者: Liu L.1, Zhang Y.1
-
隶属关系:
- School of Mathematics
- 期: 卷 103, 编号 3-4 (2018)
- 页面: 415-429
- 栏目: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/150672
- DOI: https://doi.org/10.1134/S0001434618030082
- ID: 150672
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详细
For positive integers c, s ≥ 1, r ≥ 3, let Wr(c, s) be the least integer such that if a set of at least Wr(c, s) points in the plane, no three of which are collinear, is colored with c colors, then this set contains a monochromatic r-gon with at most s interior points. As is known, if r = 3, then Wr(c, s)=Wr(c, s). In this paper, we extend these results to the case r = 4. We prove that W4(2, 1) = 11, W4(3, 2) ≤ 120, and the least integer μ4(c) such that W4(c, μ4(c)) < ∞ is bounded by \(\left\lfloor {\frac{{c - 1}}{2}} \right\rfloor \cdot 2 \leqslant \mu 4\left( c \right) \leqslant 2c - 3\),where c ≥ 2.
作者简介
L. Liu
School of Mathematics
编辑信件的主要联系方式.
Email: liuling00ling@163.com
中国, Tianjin
Y. Zhang
School of Mathematics
Email: liuling00ling@163.com
中国, Tianjin
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