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Embedding simply connected 2-complexes in 3-space -- I. A Kuratowski-type characterisation

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arxiv 1709.04642 v3 pith:LUTO6MG6 submitted 2017-09-14 math.CO math.GT

Johannes Carmesin This is my paper · ORCID
classification math.COmath.GT
keywords connectedcharacterisationcomplexessimplyspaceanalogousanswerscharacterise
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We characterise the embeddability of simply connected locally 3-connected 2-dimensional simplicial complexes in 3-space in a way analogous to Kuratowski's characterisation of graph planarity, by excluded minors. This answers questions of Lov\'asz, Pardon and Wagner.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Monotone Clustered Level Planarity

    cs.DS 2026-07 conditional novelty 7.0 of 10

    mCLP is NP-complete even on constant-size-tree forests with bounded levels or clusters, and FPT when parameterized by vertex cover number plus number of clusters.

  2. Representing Graphs and Hypergraphs by Touching Polygons in 3D

    cs.CG 2019-08 reject novelty 7.0 of 10

    All graphs with minimum degree at least three admit corner-touching convex polygon representations in 3D, with polynomial-grid algorithms for bipartite, cubic, and 1-planar cubic graphs and impossibility results for S...

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