# 4-regular planar unit triangle graphs without additional triangles

## TL;DR

This paper proves the existence of 4-regular planar graphs made solely of unit triangles, with the smallest such graph having at most 6422 triangles, advancing understanding of geometric graph constructions.

## Contribution

It demonstrates the existence of 4-regular planar unit triangle graphs without extra triangles and provides an upper bound on their size.

## Key findings

- Existence of 4-regular planar unit triangle graphs proven.
- Smallest such graph has at most 6422 triangles.
- No additional triangles are needed in these graphs.

## Abstract

In this article we proof the existence of 4-regular planar unit-distance graphs consisting only of unit triangles without additional triangles. It is shown that the smallest number of unit triangles is $\leq$6422.

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Source: https://tomesphere.com/paper/1902.00966