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

## TL;DR

This paper establishes a new lower bound, better than linear, for the minimum diameter of planar integral point sets in semi-general position, advancing understanding of their geometric constraints.

## Contribution

It introduces a novel lower bound for the diameter of semi-general position point sets, improving upon previous linear bounds.

## Key findings

- New lower bound for diameter surpasses linear growth
- Improved understanding of geometric constraints in integral point sets
- Advances theoretical bounds in Euclidean geometry

## 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.