4-regular planar unit triangle graphs without additional triangles
Mike Winkler, Peter Dinkelacker, Stefan Vogel

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.
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 6422.
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Taxonomy
TopicsStructural Analysis and Optimization · Computational Geometry and Mesh Generation · Advanced Graph Theory Research
