[math-fun] regular matchstick graph

From: Veit Elser <ve10@cornell.edu> https://en.wikipedia.org/wiki/Matchstick_graph "Harborth graph"

--in order for a K-regular matchstick graph to exist with N vertices, we need 2N coordinates to satisfy K*N/2 equations. And actually the first two vertices can wlog be located at (0,0) and (1,0) in which case 2N-4 coordinates must satisfy K*N/2-1 equations. The #equations is arbitrarily greater than the #unknowns if K>=5 when N=large, therefore perhaps K>=5 is impossible? If K=4 it also is greater, but only by 3, so a few miracles like Harborth's could be hoped for. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)