English

On diameter bounds for planar integral point sets in semi-general position

Combinatorics 2019-07-23 v1

Abstract

A point set MM in the Euclidean plane is called a planar integral point set if all the distances between the elements of MM are integers, and MM is not situated on a straight line. A planar integral point set is called to be in semi-general position, if it does not contain collinear triples. The existing lower bound for mininum diameter of planar integral point sets is linear. We prove a new lower bound for mininum diameter of planar integral point sets in semi-general position that is better than linear.

Keywords

Cite

@article{arxiv.1907.09331,
  title  = {On diameter bounds for planar integral point sets in semi-general position},
  author = {N. N. Avdeev},
  journal= {arXiv preprint arXiv:1907.09331},
  year   = {2019}
}
R2 v1 2026-06-23T10:27:10.461Z