Papers, explained

Summaries

Short, self-contained overviews of some of my papers — the questions they start from and what they prove.

Linked & lean tree-decompositions
Kříž and Thomas proved that every graph of finite tree-width has a lean tree-decomposition of the same width. We ask — and largely answer — what survives when the width itself is infinite.
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Typical graphs
Which infinitely edge-connected graphs are unavoidable? For strong immersions the answer turns out to be a single graph — the halved Farey graph.
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Trees of tangles in locally finite graphs
Robertson and Seymour's tree-of-tangles theorem, extended to locally finite graphs — with thick ends pinned down as the exact obstruction.
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Common cyclic structure
When do k prescribed edges of a graph lie on a common circuit? A clean global answer, phrased entirely in terms of odd cuts.
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A Cantor-Bernstein Result for Trees
If a graph packs λ edge-disjoint spanning trees and is also covered by λ spanning trees, does it split into exactly λ of them? A Cantor–Bernstein-style yes.
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