English

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.

Keywords

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

R2 v1 2026-06-22T07:57:33.250Z