English

APUD(1,1) Recognition in Polynomial Time

Computational Geometry 2022-10-11 v1

Abstract

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 kk horizontal and mm vertical lines, an APUD(k,mk,m) is a unit disk graph such that each unit disk is centered either on a given horizontal or vertical line. \c{C}a\u{g}{\i}r{\i}c{\i} showed in 2020 that APUD(k,mk,m) recognition is NP-hard. In this paper, we show that APUD(1,11,1) recognition is polynomial time solvable.

Keywords

Cite

@article{arxiv.2210.04090,
  title  = {APUD(1,1) Recognition in Polynomial Time},
  author = {Deniz Ağaoğlu Çağırıcı and Onur Çağırıcı},
  journal= {arXiv preprint arXiv:2210.04090},
  year   = {2022}
}
R2 v1 2026-06-28T03:04:24.940Z