473 citations · 2k across the 152 of their papers we have counts for
164 papers
The Erdős--Sós Theorem
David R. Wood
We present an exposition of a proof, discovered by GPT-6 Astra, of the Erdős--Sós Conjecture, which states that every graph with average degree greater than contains every tr…
Clustered Colouring of Odd--Minor-Free Graphs
Robert Hickingbotham, Dong Yeap Kang, Sang-il Oum +2
The clustered chromatic number of a graph class is the minimum integer such that every graph has a -colouring where each monochromatic compon…
Powers of planar graphs, product structure, and blocking partitions
Marc Distel, Robert Hickingbotham, Michał T. Seweryn +1
We prove that the -power of any planar graph is contained in for some graph with bounded treewidth, some path , and some functio…
The grid-minor theorem revisited
Vida Dujmović, Robert Hickingbotham, Jędrzej Hodor +6
We prove that for every planar graph of treedepth , there exists a positive integer such that for every -minor-free graph , there exists a graph of treewidth a…
Proof of the Clustered Hadwiger Conjecture
Vida Dujmović, Louis Esperet, Pat Morin +1
Hadwiger's Conjecture asserts that every -minor-free graph is properly -colourable. We prove the following improper analogue of Hadwiger's Conjecture: for fixed , ev…
The Excluded Tree Minor Theorem Revisited
Vida Dujmović, Robert Hickingbotham, Gwenaël Joret +3
We prove that for every tree of radius , there is an integer such that every -minor-free graph is contained in for some graph with pathwidth at m…