A probabilistic Hadwiger-Nelson problem
Combinatorics
2015-01-13 v1
Abstract
If you color a table using k colors, and throw a needle randomly on it, for some proper definition, you get a certain probability that the endpoints will fall on different colors. How can one make this probability maximal? This problem is related to finite graphs having unit-length edges, and some bounds on the optimal probability are deduced.
Cite
@article{arxiv.1501.02441,
title = {A probabilistic Hadwiger-Nelson problem},
author = {Thomas Bourgeat and Marc Heinrich and Paul Melotti and Jean-Marc Robert},
journal= {arXiv preprint arXiv:1501.02441},
year = {2015}
}
Comments
11 pages, 5 figures