论文标题
密切绑定了火柴形图的边缘数量
A tight bound for the number of edges of matchstick graphs
论文作者
论文摘要
Matchstick图是一个平面图，其边缘为单位距离线段。 Harbourth在1981年介绍了这些图形，并猜想$ n $ Vertices上的火柴图的最大边数为$ \ lfloor 3n- \ sqrt {12n-3} \ rfloor $。在本文中，我们证明了所有$ n \ geq 1 $的猜想。证明的主要几何成分是与L'Huilier的不平等有关的等等不平等。
A matchstick graph is a plane graph with edges drawn as unit-distance line segments. Harborth introduced these graphs in 1981 and conjectured that the maximum number of edges for a matchstick graph on $n$ vertices is $\lfloor 3n-\sqrt{12n-3} \rfloor$. In this paper we prove this conjecture for all $n\geq 1$. The main geometric ingredient of the proof is an isoperimetric inequality related to L'Huilier's inequality.
