# Most Classic Problems Remain NP-hard on Relative Neighborhood Graphs and their Relatives

@article{Kunz2021MostCP, title={Most Classic Problems Remain NP-hard on Relative Neighborhood Graphs and their Relatives}, author={Pascal Kunz and Till Fluschnik and Rolf Niedermeier and Malte Renken}, journal={ArXiv}, year={2021}, volume={abs/2107.04321} }

Proximity graphs have been studied for several decades, motivated by applications in computational geometry, geography, data mining, and many other fields. However, the computational complexity of classic graph problems on proximity graphs mostly remained open. We now study 3-Colorability, Dominating Set, Feedback Vertex Set, Hamiltonian Cycle, and Independent Set on the proximity graph classes relative neighborhood graphs, Gabriel graphs, and relatively closest graphs. We prove that all of the…

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