On diameter bounds for planar integral point sets in semi-general position
Abstract
A point set $M$ in the Euclidean plane is called a planar integral point set if all the distances between the elements of $M$ are integers, and $M$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2019
- DOI:
- 10.48550/arXiv.1907.09331
- arXiv:
- arXiv:1907.09331
- Bibcode:
- 2019arXiv190709331A
- Keywords:
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- Mathematics - Combinatorics;
- 52C10