Lines in the plane and decompositions of graphs

Abstract

Whether Sylvester himself had a proof is in doubt, but a correct proof was given by Tibor Gallai [Grünwald] some 40 years later. Therefore the following theorem is commonly attributed to Sylvester and Gallai. Subsequent to Gallai’s proof several others appeared, but the following argument due to L. M. Kelly may be “simply the best.”