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pro vyhledávání: '"Carmesin, Johannes"'
A recent development in graph theory is to study local separators, vertex sets that need not separate graphs globally but just locally. We use this idea to conjecture an extension of Stallings' theorem to finite nilpotent groups. We provide an exampl
Externí odkaz:
http://arxiv.org/abs/2403.07776
Autor:
Carmesin, Johannes, Frenkel, Sarah
Graph decompositions are the natural generalisation of tree decompositions where the decomposition tree is replaced by a genuine graph. Recently they found theoretical applications in the theory of sparsity, topological graph theory, structural graph
Externí odkaz:
http://arxiv.org/abs/2312.12354
Autor:
Carmesin, Johannes
Firstly, 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 nine excluded minors. This answers questions o
Externí odkaz:
http://arxiv.org/abs/2309.15504
Autor:
Carmesin, Johannes, Kurkofka, Jan
Every large $k$-connected graph-minor induces a $k$-tangle in its ambient graph. The converse holds for $k\le 3$, but fails for $k\ge 4$. This raises the question whether `$k$-connected' can be relaxed to obtain a characterisation of $k$-tangles thro
Externí odkaz:
http://arxiv.org/abs/2309.00902
Autor:
Carmesin, Johannes, Kurkofka, Jan
We offer a new structural basis for the theory of 3-connected graphs, providing a unique decomposition of every such graph into parts that are either quasi 4-connected, wheels, or thickened $K_{3,m}$'s. Our construction is explicit, canonical, and ha
Externí odkaz:
http://arxiv.org/abs/2304.00945
Autor:
Carmesin, Johannes
We prove that simply connected local 2-dimensional simplicial complexes embed in 3-space if and only if their dual matroids are graphic. Examples are provided that the assumptions of simply connectedness and locality are necessary. This may be regard
Externí odkaz:
http://arxiv.org/abs/2210.15594
Autor:
Carmesin, Johannes
A graph $H$ is ubiquitous if for every graph $G$ that for every natural number $n$ contains $n$ vertex-disjoint $H$-minors contains infinitely many vertex-disjoint $H$-minors. Andreae conjectured that every locally finite graph is ubiquitous. We give
Externí odkaz:
http://arxiv.org/abs/2210.02711
Autor:
Carmesin, Johannes, Kurkofka, Jan
Robertson and Seymour constructed for every graph $G$ a tree-decomposition that efficiently distinguishes all the tangles in $G$. While all previous constructions of these decompositions are either iterative in nature or not canonical, we give an exp
Externí odkaz:
http://arxiv.org/abs/2205.11488
We extend Heawood's theorem on the colourability of plane triangulations to triangulations of 3-space. We prove that a triangulation of 3-space can be edge coloured with three colours if and only if all edges have even degree.
Externí odkaz:
http://arxiv.org/abs/2204.02858
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 i
Externí odkaz:
http://arxiv.org/abs/2103.15404