Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Albrechtsen, Sandra"'
We prove that there is a function $f$ such that every graph with no $K$-fat $K_4$ minor is $f(K)$-quasi-isometric to a graph with no $K_4$ minor. This solves the $K_4$-case of a general conjecture of Georgakopoulos and Papasoglu. Our proof technique
Externí odkaz:
http://arxiv.org/abs/2408.15335
Autor:
Albrechtsen, Sandra
We extend Robertson and Seymour's tangle-tree duality theorem to infinite graphs.
Externí odkaz:
http://arxiv.org/abs/2405.06756
Kriz and Thomas showed that every (finite or infinite) graph of tree-width $k \in \mathbb{N}$ admits a lean tree-decomposition of width $k$. We discuss a number of counterexamples demonstrating the limits of possible generalisations of their result t
Externí odkaz:
http://arxiv.org/abs/2405.06755
We prove that every graph which admits a tree-decomposition into finite parts has a rooted tree-decomposition into finite parts that is linked, tight and componental. As an application, we obtain that every graph without half-grid minor has a lean tr
Externí odkaz:
http://arxiv.org/abs/2405.06753
Autor:
Albrechtsen, Sandra
Carmesin and Gollin proved that every finite graph has a canonical tree-decomposition $(T, \mathcal{V})$ of adhesion less than $k$ that efficiently distinguishes every two distinct $k$-profiles, and which has the further property that every separable
Externí odkaz:
http://arxiv.org/abs/2403.19585
Autor:
Albrechtsen, Sandra, Diestel, Reinhard, Elm, Ann-Kathrin, Fluck, Eva, Jacobs, Raphael W., Knappe, Paul, Wollan, Paul
Given an arbitrary class $\mathcal{H}$ of graphs, we investigate which graphs admit a decomposition modelled on a graph in $\mathcal{H}$ into parts of small radius. The $\mathcal{H}$-decompositions that we consider here generalise the notion of tree-
Externí odkaz:
http://arxiv.org/abs/2307.08497
Publikováno v:
SIAM Journal on Discrete Mathematics Volume 38 Issue 2 (June 2024), Pages: 1438 - 1450
We give an approximate Menger-type theorem for when a graph $G$ contains two $X-Y$ paths $P_1$ and $P_2$ such that $P_1 \cup P_2$ is an induced subgraph of $G$. More generally, we prove that there exists a function $f(d) \in O(d)$, such that for ever
Externí odkaz:
http://arxiv.org/abs/2305.04721
Autor:
Albrechtsen, Sandra
We combine the two fundamental fixed-order tangle theorems of Robertson and Seymour into a single theorem that implies both, in a best possible way. We show that, for every $k \in \mathbb{N}$, every tree-decomposition of a graph $G$ which efficiently
Externí odkaz:
http://arxiv.org/abs/2304.12078
Autor:
Albrechtsen, Sandra
Robertson and Seymour proved two fundamental theorems about tangles in graphs: the tree-of-tangles theorem, which says that every graph has a tree-decomposition such that distinguishable tangles live in different nodes of the tree, and the tangle-tre
Externí odkaz:
http://arxiv.org/abs/2302.01808
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