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

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arxiv 1709.04659 v3 pith:XLYPICHK submitted 2017-09-14 math.CO math.GT

Johannes Carmesin This is my paper · ORCID
classification math.COmath.GT
keywords characterisationconnectedlistobstructionsseriessimplyspaceanalogue
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This paper is the last paper in a series of five papers. Building on earlier papers in this series, we prove an analogue of Kuratowski's characterisation of graph planarity for three dimensions. More precisely, a simply connected 2-dimensional simplicial complex embeds in 3-space if and only if it has no obstruction from an explicit list of obstructions. This list of obstructions is finite except for one infinite family.

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  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.

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