TY - JOUR
T1 - Uniformly Discrete Forests with Poor Visibility
AU - Alon, Noga
N1 - Publisher Copyright:
© 2017 Cambridge University Press.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - We prove that there is a set F in the plane so that the distance between any two points of F is at least 1, and for any positive ϵ < 1, and every line segment in the plane of length at least ϵ-1-o(1), there is a point of F within distance ϵ of the segment. This is tight up to the o(1)-term in the exponent, improving earlierestimates of Peres, of Solomon and Weiss, and of Adiceam.
AB - We prove that there is a set F in the plane so that the distance between any two points of F is at least 1, and for any positive ϵ < 1, and every line segment in the plane of length at least ϵ-1-o(1), there is a point of F within distance ϵ of the segment. This is tight up to the o(1)-term in the exponent, improving earlierestimates of Peres, of Solomon and Weiss, and of Adiceam.
UR - http://www.scopus.com/inward/record.url?scp=85030864065&partnerID=8YFLogxK
U2 - 10.1017/S0963548317000505
DO - 10.1017/S0963548317000505
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AN - SCOPUS:85030864065
SN - 0963-5483
VL - 27
SP - 442
EP - 448
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 4
ER -