9 papers
Tree-partitions and small-spread tree-decompositions
Marc Distel, Neel Kaul, Raj Kaul +1
Tree-decompositions and treewidth are of fundamental importance in structural and algorithmic graph theory. The "spread" of a tree-decomposition is the minimum integer such tha…
A coarse Gallai theorem
Marc Distel, Ugo Giocanti, JÄdrzej Hodor +2
We prove that there exist functions and such that for all positive integers and , for every graph and every subset of the vertices of , either contain…
Small counterexamples to the fat minor conjecture
Sandra Albrechtsen, Marc Distel, Agelos Georgakopoulos
We narrow the gap between the family of graphs that do and the family of graphs that do not satisfy the fat minor conjecture by obtaining much simpler counterexamples than were pre…
An alternative characterisation of graphs quasi-isometric to graphs of bounded treewidth
Marc Distel
Quasi-isometry is a measure of how similar two graphs are at `large-scale'. Nguyen, Scott, and Seymour [arXiv:2501.09839] and Hickingbotham [arXiv:2501.10840] independently gave a…
Excluding as a fat minor
Sandra Albrechtsen, Marc Distel, Agelos Georgakopoulos
We prove that for every , the graph satisfies the fat minor conjecture of Georgakopoulos and Papasoglu: for every there exist $M,A\in…
Graphs Excluding a Minor in Blowups of Treewidth 3 Graphs
Marc Distel
Alon, Seymour, and Thomas [J. Amer. Math. Soc. 1990] famously showed that every -vertex -minor-free graph has treewidth . Recently, Distel, DujmoviÄ, Eppste…