Product structure extension of the Alon–Seymour–Thomas theorem.
M. Distel,
V. Dujmović,
D. Eppstein,
R. Robert Hickingbotham,
G. Joret,
P. Micek,
P. Morin,
M. T. Seweryn, and
D. R. Wood.
arXiv:2212.08739.
SIAM J. Discrete
Math. 38 (3): 2095–2107, 2024, doi:10.1137/23M1591773.
The graphs in any nontrivial minor-closed graph family can be represented as strong products of a graph of treewidth 4 with a clique of size \(O(\sqrt{n})\). For planar graphs and \(K_{3,t}\)-minor-free graphs, the treewidth can be reduced to 2. An earlier version of the preprint with only the first part of these results used a different title, "Graphs excluding a fixed minor are \(O(\sqrt{n})\)-complete-blowups of a treewidth 4 graph".