Geodesic
Outerspatial 2-complexes: extending the class of outerplanar graphs to three dimensions
Johannes Carmesin1 ; Tsvetomir Mihaylov1
1University of Birmingham
The electronic journal of combinatorics, Tome 30 (2023) no. 3
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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 $K_4$ or $K_{2,3}$. 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.
DOI : 10.37236/10539
Classification : 05C10, 05E45, 05C60
Mots-clés : nested plane embedding, embeddings of 2-complexes in 3-space

Johannes Carmesin  1   ; Tsvetomir Mihaylov  1

1 University of Birmingham 
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     title = {Outerspatial 2-complexes: extending the class of outerplanar graphs to three dimensions},
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Johannes Carmesin; Tsvetomir Mihaylov. Outerspatial 2-complexes: extending the class of outerplanar graphs to three dimensions. The electronic journal of combinatorics, Tome 30 (2023) no. 3. doi: 10.37236/10539

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