Computational topology of graphs on surfaces
Computational Geometry
2017-09-06 v2 Discrete Mathematics
Data Structures and Algorithms
Algebraic Topology
Combinatorics
Abstract
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn on surfaces. Typical questions include representing surfaces and graphs embedded on them computationally, deciding whether a graph embeds on a surface, solving computational problems related to homotopy, optimizing curves and graphs on surfaces, and solving standard graph algorithm problems more efficiently in the case of surface-embedded graphs.
Cite
@article{arxiv.1702.05358,
title = {Computational topology of graphs on surfaces},
author = {Éric Colin de Verdière},
journal= {arXiv preprint arXiv:1702.05358},
year = {2017}
}
Comments
To appear in the Handbook of Discrete and Computational Geometry, 3rd edition. Minor changes compared to previous version