Welcome to mikematics.de

On this website I present some of my work, thoughts and ideas on selected topics in mathematics. These range from conjectures over abstract ideas to rigorous proofs. My main fields of research are number theory and graph theory. If a problem has grabbed me, I worked on it over many years. My favorite topics are the 3x + 1 problem and regular matchstick graphs.

In the hope to enrich the mathematical world a little bit, enjoy reading and exploring.

Mike Winkler

Latest research results

New minimal 4-regular planar unit triangle graph without additional triangles. This rigid graph consists of 6422 unit triangles and has a rotational symmetry of order 169 (Pic1 Pic2) (arXiv 1902.00966).

New minimal 3-regular matchstick graphs of girth 5. The currently smallest example consists of 54 vertices and has a point symmetry. Graph links: (54), (58), (60), (64a, 64b), (66a, 66b, 66c), (68a, 68b, 68c).

New paper: A 3-regular matchstick graph of girth 5 consisting of 54 vertices.
New paper: A catalog of 3-regular matchstick graphs of girth 5 consisting of 54 – 68 vertices

Please view the above graphs with the
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