30 citations · 53 across the 12 of their papers we have counts for
17 papers
CAT(0) square complexes that do not embed into finite products of trees
James Davies, Harry Petyt
Answering a question of Chepoi and Hagen, we give two constructions of bounded degree CAT(0) square complexes that cannot be isometrically embedded into any finite product of trees…
Surfaces without quasi-isometric simplicial triangulations
James Davies
We construct a complete Riemannian surface that admits no triangulation such that the inclusion is a quasi-isometry, where is…
Chromatic number of spacetime
James Davies
We observe that an old theorem of Graham implies that for any positive integer , there exists some positive integer such that every -colouring of contai…
Prime and polynomial distances in colourings of the plane
James Davies, Rose McCarty, Michał Pilipczuk
We give two extensions of the recent theorem of the first author that the odd distance graph has unbounded chromatic number. The first is that for any non-constant polynomial w…
Pivot-minors and the Erdős-Hajnal conjecture
James Davies
We prove a conjecture of Kim and Oum that every proper pivot-minor-closed class of graphs has the strong Erdős-Hajnal property. More precisely, for every graph , there exists $ε…
Odd distances in colourings of the plane
James Davies
We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd distance from each other.
Separating polynomial -boundedness from -boundedness
Marcin Briański, James Davies, Bartosz Walczak
Extending the idea from the recent paper by Carbonero, Hompe, Moore, and Spirkl, for every function with and $f(n)\geq\binom…
A solution to Ringel's circle problem
James Davies, Chaya Keller, Linda Kleist +2
We construct families of circles in the plane such that their tangency graphs have arbitrarily large girth and chromatic number. This provides a strong negative answer to Ringel's…
Grounded L-graphs are polynomially -bounded
James Davies, Tomasz Krawczyk, Rose McCarty +1
A grounded L-graph is the intersection graph of a collection of "L" shapes whose topmost points belong to a common horizontal line. We prove that every grounded L-graph with clique…
Improved bounds for colouring circle graphs
James Davies
We prove the first -bounding function for circle graphs that is optimal up to a constant factor. To be more precise, we prove that every circle graph with clique number at most…
Triangle-free graphs with large chromatic number and no induced wheel
James Davies
A wheel is a graph consisting of an induced cycle of length at least four and a single additional vertex with at least three neighbours on the cycle. We prove that no Burling graph…
Colouring polygon visibility graphs and their generalizations
James Davies, Tomasz Krawczyk, Rose McCarty +1
Curve pseudo-visibility graphs generalize polygon and pseudo-polygon visibility graphs and form a hereditary class of graphs. We prove that every curve pseudo-visibility graph with…
Box and segment intersection graphs with large girth and chromatic number
James Davies
We prove that there are intersection graphs of axis-aligned boxes in and intersection graphs of straight lines in that have arbitrarily large girth an…
Vertex-minor-closed classes are -bounded
James Davies
We prove a conjecture of Geelen that every proper vertex-minor-closed class of graphs is -bounded.
Locally Hamiltonian graphs and minimal size of maximal graphs on a surface
James Davies, Carsten Thomassen
We prove that every locally Hamiltonian graph with vertices and possibly with multiple edges has at least edges with equality if and only if it triangulates the sph…
Edge-maximal graphs on orientable and some non-orientable surfaces
James Davies, Florian Pfender
We study edge-maximal, non-complete graphs on surfaces that do not triangulate the surface. We prove that there is no such graph on the projective plane , is…
Circle graphs are quadratically -bounded
James Davies, Rose McCarty
We prove that the chromatic number of a circle graph with clique number is at most .