论文标题
多项式时间的APUD（1,1）识别
APUD(1,1) Recognition in Polynomial Time
论文作者
论文摘要
单位磁盘图是欧几里德平面中单位半径磁盘的相交图。 1998年，Breu和Kirkpatrick表明单位磁盘图的识别问题是NP-HARD。给定$ K $水平和$ m $垂直线，APUD（$ K，M $）是单元磁盘图，因此每个单元磁盘都以给定的水平或垂直线为中心。 Çağırıcı在2020年表明Apud（$ k，m $）的识别是NP-HARD。在本文中，我们表明Apud（$ 1,1 $）的识别是可以解决多项式时间的。
A unit disk graph is the intersection graph of a set of disk of unit radius in the Euclidean plane. In 1998, Breu and Kirkpatrick showed that the recognition problem for unit disk graphs is NP-hard. Given $k$ horizontal and $m$ vertical lines, an APUD($k,m$) is a unit disk graph such that each unit disk is centered either on a given horizontal or vertical line. Çağırıcı showed in 2020 that APUD($k,m$) recognition is NP-hard. In this paper, we show that APUD($1,1$) recognition is polynomial time solvable.
