In this paper, we show that it is NP-hard to determine whether a given graph admits a min-1-planar drawing. A drawing of a graph is min-$k$-planar if, for every crossing in the drawing, at least one of the two crossing edges involves at most $k$ crossings. This notion of min-$k$-planarity was introduced by Binucci, Büngener, Di Battista, Didimo, Dujmović, Hong, Kaufmann, Liotta, Morin, and Tappini [GD 2023; JGAA, 2024] as a generalization of $k$-planarity.

翻译：本文证明，判断给定图是否具有最小-1-平面绘制是NP难的。图的绘制称为最小-k-平面绘制，若对于其中的每个交叉点，两条交叉边中至少有一条涉及至多k个交叉。这一最小-k-平面性的概念由Binucci、Büngener、Di Battista、Didimo、Dujmović、Hong、Kaufmann、Liotta、Morin和Tappini [GD 2023; JGAA, 2024]作为k-平面性的一种推广而提出。