Graph augmentation problems are motivated by network design and have been studied extensively in optimization. We consider augmentation problems over plane geometric graphs, that is, graphs given with a crossing-free straight-line embedding in the plane. The geometric constraints on the possible new edges render some of the simplest augmentation problems intractable, and in many cases only extremal results are known. We survey recent results, highlight common trends, and gather numerous conjectures and open problems.
CITATION STYLE
Hurtado, F., & Tóth, C. D. (2014). Plane geometric graph augmentation: A generic perspective. In Thirty Essays on Geometric Graph Theory (pp. 327–354). Springer New York. https://doi.org/10.1007/978-1-4614-0110-0_17
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