We provide two constructions for $t$ edge-disjoint maximal outerplanar graphs on every number of $n \geq 4t$ vertices. The bound on the minimum number of vertices is tight. These constructions yield the existence of optimal outerthickness-$t$ graphs for every $t \in \mathbb{N}$. While one of the constructions works for all values of $t$ and extends graphs from Guy and Nowakowski (1990), the other one holds only for powers of $2$, but yields graphs with maximum degree logarithmic in the number of vertices. Thus, the latter may be helpful in tackling the open question of determining the outerthickness of all complete graphs.

翻译：我们针对所有满足 $n \geq 4t$ 的顶点数 $n$，提出了两种构造 $t$ 个边不相交极大外平面图的方法。该顶点数下界是最优的。这些构造证明了对于任意 $t \in \mathbb{N}$，最优外厚度-$t$ 图的存在性。其中一种构造适用于所有 $t$ 值，并推广了 Guy 和 Nowakowski（1990）的图；另一种构造仅适用于 $2$ 的幂次，但能生成最大度关于顶点数为对数量级的图。因此，后者可能有助于解决确定所有完全图外厚度这一开放性问题。