43 citations · 147 across the 33 of their papers we have counts for
6 papers · 1 filter
Embedding simply connected 2-complexes in 3-space -- IV. Dual matroids
Johannes Carmesin
We introduce dual matroids of 2-dimensional simplicial complexes. Under certain necessary conditions, duals matroids are used to characterise embeddability in 3-space in a way anal…
Embedding simply connected 2-complexes in 3-space -- III. Constraint minors
Johannes Carmesin
We characterise the following property by six obstructions: given a graphic matroid and a set of its elements, when is the cycle matroid of a graph such that is…
Embedding simply connected 2-complexes in 3-space -- V. A refined Kuratowski-type characterisation
Johannes Carmesin
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 thr…
Embedding simply connected 2-complexes in 3-space -- II. Rotation systems
Johannes Carmesin
We prove that 2-dimensional simplicial complexes whose first homology group is trivial have topological embeddings in 3-space if and only if there are embeddings of their link grap…
Embedding simply connected 2-complexes in 3-space -- I. A Kuratowski-type characterisation
Johannes Carmesin
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…
On tree-decompositions of one-ended graphs
Johannes Carmesin, Florian Lehner, Rögnvaldur G. Möller
A graph is one-ended if it contains a ray (a one way infinite path) and whenever we remove a finite number of vertices from the graph then what remains has only one component which…