2020/07/07 by Nicolas Grelier, Grelier, Nicolas
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Graph Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2007.03492
openalex publication_date 2020/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the 90's Clark, Colbourn and Johnson wrote a seminal paper where they proved that maximum clique can be solved in polynomial time in unit disk graphs. Since then, the complexity of maximum clique in intersection graphs of d-dimensional (unit) balls has been investigated. For ball graphs, the problem is NP-hard, as shown by Bonamy et al. (FOCS '18). They also gave an efficient polynomial time approximation scheme (EPTAS) for disk graphs. However, the complexity of maximum clique in this setting remains unknown. In this paper, we show the existence of a polynomial time algorithm for a geometric superclass of unit disk graphs. Moreover, we give partial results toward obtaining an EPTAS for intersection graphs of convex pseudo-disks.