Graph Embeddings in Spherical Maps

Home

Discover

Bookmarks

Keep Up With Latest Trending Papers. Computer Science, AI and Machine Learning and more.Subscribe

CC BY-SA

Source arXiv

Combinatorics

Logic in Computer Science

Graph Embeddings in Spherical Maps

On Homotopy of Walks and Spherical Maps in Homotopy Type Theory

This article presents a refinement of one characterisation of embeddings in the sphere, called spherical maps, of connected and directed multigraphs with discrete node sets.

A combinatorial notion of homotopy for walks and the normalform of walks under a reduction relation is introduced.

The first characterisation of spherical maps states that a graph can be embedded in the sphere if any pair of walks with the same endpoints are merely walk-homotopic.

The refinement of this definition filters out any walk with inner cycles.

Authors

Jonathan Prieto-Cubides

◐ Recommended Follows

◐ Latest Activity