We show that a matchstick graph with $n$ vertices has no more than $3n-c\sqrt{n-1/4}$ edges, where $c=\frac12(\sqrt{12} + \sqrt{2\pi\sqrt{3}})$. The main tools in the proof are the Euler formula, the isoperimetric inequality, and an upper bound for the number of edges in terms of $n$ and the number of non-triangular faces. We also find a sharp upper bound for the number of triangular faces in a matchstick graph.

翻译：我们显示一个配有$n的顶点的火柴图没有超过$3n-c\sqrt{n-1/4}美元边缘, 也就是 ${sqrt{12} +\sqrt{2\pi\sqrt{3}$。 证据中的主要工具是 Euler 公式、 等光度不平等, 以及以 $ 和非三角形面数表示的边缘数的上限。 我们还在匹配点图中发现了三角形面数的垂直上限 。