Outerspatial 2-complexes: Extending the class of outerplanar graphs to three dimensions
Combinatorics
2023-03-31 v3
Abstract
We introduce the class of outerspatial 2-complexes as the natural generalisation of the class of outerplanar graphs to three dimensions. Answering a question of O-joung Kwon, we prove that a locally 2-connected 2-complex is outerspatial if and only if it does not contain a surface of positive genus as a subcomplex and does not have a space minor that is a generalised cone over or . This is applied to nested plane embeddings of graphs; that is, plane embeddings constrained by conditions placed on a set of cycles of the graph.
Keywords
Cite
@article{arxiv.2103.15404,
title = {Outerspatial 2-complexes: Extending the class of outerplanar graphs to three dimensions},
author = {Johannes Carmesin and Tsvetomir Mihaylov},
journal= {arXiv preprint arXiv:2103.15404},
year = {2023}
}