Unit distance graphs and matchstick graphs
Articles
Realized Rank Certificates for Matchstick Frameworks and Insertion Edges (2026)
Approximate Solutions of 4-regular Matchstick Graphs with 51 – 62 Vertices (2020)
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 catalog 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
Latest research
Software
Streichholzgraphen-Rechner – Main program (German)
Matchstick Graphs Calculator (MGC)
These free tools facilitate the construction and analysis of unit distance and matchstick graphs directly in your web browser. It verifies whether a planar graph’s edges are equilateral or if a unit-distance embedding can be achieved by adjusting angles. While the numerical results do not constitute a rigorous mathematical proof, they provide strong evidence that a formal proof is attainable.
The graphs discussed in the articles above can be visualized using the MGC, which also provides data for a constructive proof for each example.