APUD(1,1) Recognition in Polynomial Time
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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.
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