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20242026
most citedOdd coloring graphs with linear neighborhood complexity

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math.CO2024

Counterexample to Babai's lonely colour conjecture

James Davies, Meike Hatzel, Liana Yepremyan

Motivated by colouring minimal Cayley graphs, in 1978, Babai conjectured that no-lonely-colour graphs have bounded chromatic number. We disprove this in a strong sense by construct…

math.CO2024

Fat minors cannot be thinned (by quasi-isometries)

James Davies, Robert Hickingbotham, Freddie Illingworth +1

We disprove the conjecture of Georgakopoulos and Papasoglu that a length space (or graph) with no -fat minor is quasi-isometric to a graph with no minor. Our counterexam…