4 papers · 1 filter
A short derivation of the structure theorem for graphs with excluded topological minors
Joshua Erde, Daniel Weißauer
As a major step in their proof of Wagner's conjecture, Robertson and Seymour showed that every graph not containing a fixed graph as a minor has a tree-decomposition in which e…
Structural submodularity and tangles in abstract separation systems
Reinhard Diestel, Joshua Erde, Daniel Weißauer
We prove a tangle-tree theorem and a tangle duality theorem for abstract separation systems that are submodular in the structural sense that, for every pair of oriented se…
In absence of long chordless cycles, large tree-width becomes a local phenomenon
Daniel Weißauer
We prove that, for all and , every graph of sufficiently large tree-width contains either a complete bipartite graph or a chordless cycle of length greater than…
Algebraically grid-like graphs have large tree-width
Daniel Weißauer
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…