Unit distance graphs and matchstick graphs

Articles

Approximate Solutions of 4-regular Matchstick Graphs with 51 – 62 Vertices (2019)

A catalog of 3-regular matchstick graphs of girth 5 consisting of 54 – 68 vertices (2019)

A 3-regular matchstick graph of girth 5 consisting of 54 vertices (2019)
Geombinatorics Quarterly, Volume XXIX, Issue 3, January 2020, Pages 116–121

4-regular planar unit triangle graphs without additional triangles (2019)
Geombinatorics Quarterly, Volume XXIX, Issue 2, October 2019, Pages 72–77

A catalogue of 4-regular and (2; 4)-regular matchstick graphs (2017)

On the existence of 4-regular matchstick graphs (2017)

Minimal completely asymmetric (4; n)-regular matchstick graphs (2016)

New minimal (4; n)-regular matchstick graphs (2016)
Geombinatorics Quarterly, Volume XXVII, Issue 1, July 2017, Pages 26–44

Ein neuer 4-regulärer Streichholzgraph (2016)
Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV), Band 24, Heft 2, Juli 2016, Seiten 74–75

Software

Matchstick Graphs Calculator (MGC) – a software for the construction and calculation of unit distance graphs and matchstick graphs (2016–2020).

The graphs from the articles can be viewed with the MGC, which contains also a constructive proof for each graph. This remarkable software created by Stefan Vogel runs directly in web browsers. The method Stefan Vogel used for the calculations he describes in the article: Beweglichkeit eines Streichholzgraphen bestimmen.

Research thread

Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5, Thread in a graph theory forum (2016–2020)
(Nicknames used in the forum: haribo = Peter Dinkelacker, Slash = Mike Winkler)