Regular matchstick graphs


 

On the existence of 4-regular matchstick graphs (arXiv 1705.00293 link)

A catalogue of 4-regular and (2, 4)-regular matchstick graphs (arXiv 1705.04715 link)

New minimal (4, n)-regular matchstick graphs (arXiv 1604.07134 link)

Minimal completely asymmetric (4, n)-regular matchstick graphs (arXiv 1609.06972 link)

Ein 4-regulärer Streichholzgraph mit 114 Kanten (article link) (German)

Der große Bruder des Harborth-Graphen (article link) (German)

Ein neuer 4-regulärer Streichholzgraph, Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV), Band 24, Heft 2, Seiten 74–75, ISSN (Online) 0942-5977, ISSN (Print) 0947-4471, DOI: 10.1515/dmvm-2016-0031, July 2016 (article link) (German)

Beweglichkeit eines Streichholzgraphen bestimmen (Stefan Vogel) (article link) (German)

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

 

The graphs from the above articles can be viewed with the "Matchstick Graphs Calculator" (MGC). The MCG contains also constructive proofs for the graphs. This remarkable software created by Stefan Vogel runs directly in web browsers. Just click on the program link below. The method Vogel used for the calculations he describes in his German article "Beweglichkeit eines Streichholzgraphen bestimmen".

Matchstick Graphs Calculator (MGC) - a software for the construction and calculation of matchstick graphs (program link)

 

Comming soon: matchstickgraphs.org - the world's official website about matchstick graphs.