多项式时间上的APUD（1，1）识别
APUD(1,1) Recognition in Polynomial Time
摘要：
单位圆盘图是欧氏平面上一组单位半径圆盘的交图。1998年，Breu和Kirkpatrick证明了单位圆盘图的识别问题是NP-难的。给定$k$水平线和$m$垂直线，APUD（$k,m$）是单位圆盘图，使得每个单位圆盘以给定的水平线或垂直线为中心。在2020年的研究表明，APUD（$k,m$）识别是NP难的。本文证明了APUD（$1,1$）识别是多项式时间可解的.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
