Computational topology of graphs on surfaces
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 surfaceembedded graphs.
 Publication:

arXiv eprints
 Pub Date:
 February 2017
 DOI:
 10.48550/arXiv.1702.05358
 arXiv:
 arXiv:1702.05358
 Bibcode:
 2017arXiv170205358D
 Keywords:

 Computer Science  Computational Geometry;
 Computer Science  Discrete Mathematics;
 Computer Science  Data Structures and Algorithms;
 Mathematics  Algebraic Topology;
 Mathematics  Combinatorics;
 68U05;
 05C10;
 57M15;
 68R10;
 F.2.2;
 G.2.2;
 I.3.5
 EPrint:
 To appear in the Handbook of Discrete and Computational Geometry, 3rd edition. Minor changes compared to previous version