Zobrazeno 1 - 10
of 26
pro vyhledávání: '"Weißauer, Daniel"'
Autor:
Erde, Joshua, Weißauer, Daniel
As a major step in their proof of Wagner's conjecture, Robertson and Seymour showed that every graph not containing a fixed graph $H$ as a minor has a tree-decomposition in which each torso is almost embeddable in a surface of bounded genus. Recently
Externí odkaz:
http://arxiv.org/abs/1807.01119
We prove a tangle-tree theorem and a tangle duality theorem for abstract separation systems $\vec S$ that are submodular in the structural sense that, for every pair of oriented separations, $\vec S$ contains either their meet or their join defined i
Externí odkaz:
http://arxiv.org/abs/1805.01439
Autor:
Weißauer, Daniel
We prove that, for all $\ell$ and $s$, every graph of sufficiently large tree-width contains either a complete bipartite graph $K_{s,s}$ or a chordless cycle of length greater than $\ell$.
Externí odkaz:
http://arxiv.org/abs/1803.02703
Autor:
Weißauer, Daniel
By the Grid Minor Theorem of Robertson and Seymour, every graph of sufficiently large tree-width contains a large grid as a minor. Tree-width may therefore be regarded as a measure of 'grid-likeness' of a graph. The grid contains a long cycle on the
Externí odkaz:
http://arxiv.org/abs/1802.05158
Autor:
Weißauer, Daniel
Let $G$ be a connected graph and $\ell : E(G) \to \mathbb{R}^+$ a length-function on the edges of $G$. The Steiner distance $\mathrm{sd}_G(A)$ of $A \subseteq V(G)$ within $G$ is the minimum length of a connected subgraph of $G$ containing $A$, where
Externí odkaz:
http://arxiv.org/abs/1703.09969
Autor:
Weißauer, Daniel
A $k$-block in a graph $G$ is a maximal set of at least $k$ vertices no two of which can be separated in $G$ by deleting fewer than $k$ vertices. The block number $\beta(G)$ of $G$ is the maximum integer $k$ for which $G$ contains a $k$-block. We pro
Externí odkaz:
http://arxiv.org/abs/1702.04245
Autor:
Weißauer, Daniel
Call a graph $G$ zero-forcing for a finite abelian group $\mathcal{G}$ if for every $\ell : V(G) \to \mathcal{G}$ there is a connected $A \subseteq V(G)$ with $\sum_{a \in A} \ell(a) = 0$. The problem we pose here is to characterise the class of zero
Externí odkaz:
http://arxiv.org/abs/1610.04407
Autor:
Hamann, Matthias, Weißauer, Daniel
Publikováno v:
SIAM J. Discrete Math., 30(3):1391-1400, 2016
Diestel and M\"uller showed that the connected tree-width of a graph $G$, i.e., the minimum width of any tree-decomposition with connected parts, can be bounded in terms of the tree-width of $G$ and the largest length of a geodesic cycle in $G$. We i
Externí odkaz:
http://arxiv.org/abs/1503.01592
Autor:
Weißauer, Daniel
Publikováno v:
In Journal of Combinatorial Theory, Series B November 2019 139:342-352
Publikováno v:
In Journal of Combinatorial Theory, Series A October 2019 167:155-180