6 papers
Minimal Cayley graphs with large chromatic number
James Davies, Meike Hatzel, Liana Yepremyan
Resolving Babai's minimal Cayley graph problem, we construct finite minimal Cayley graphs with arbitrarily large chromatic number.
Odd coloring graphs with linear neighborhood complexity
James Davies, Meike Hatzel, Kolja Knauer +2
We prove that any class of graphs with linear neighborhood complexity has bounded improper odd chromatic number. As a result, if is the class of all circle graphs, or…
Girth in -representable matroids
James Davies, Meike Hatzel, Kolja Knauer +2
We prove a conjecture of Geelen, Gerards, and Whittle that for any finite field and any integer , every cosimple -representable matroid with sufficiently large gi…
Strongly sublinear separators and bounded asymptotic dimension for sphere intersection graphs
James Davies, Agelos Georgakopoulos, Meike Hatzel +1
In this paper, we consider the class of sphere intersection graphs in for . We show that for each integer , the class of all graphs in $…
Quasi-isometries between graphs with variable edge lengths
James Davies, Meike Hatzel, Robert Hickingbotham
This paper investigates quasi-isometries between graphs with variable edge lengths. A quasi-isometry is a mapping between metric spaces that approximately preserves distances, allo…
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…