6 papers
String graphs are quasi-isometric to planar graphs
James Davies
We prove that for every countable string graph , there is a planar graph with such that \[ \frac{1}{23660800}d_S(u,v) \le d_G(u,v) \le 162 d_S(u,v) \] for all $u…
Counterexample to the conjectured coarse grid theorem
Sandra Albrechtsen, James Davies
We show that for every there exists a graph that does not contain the -grid as a -fat minor and is not -quasi-isometric to a g…
Burling graphs in graphs with large chromatic number
Tara Abrishami, Marcin BriaÅski, James Davies +4
A graph class is -bounded if the only way to force large chromatic number in graphs from the class is by forming a large clique. In the 1970s, ErdÅs conjectured that intersect…
Preparing graph states forbidding a vertex-minor
James Davies, Andrew Jena
Measurement based quantum computing is preformed by adding non-Clifford measurements to a prepared stabilizer states. Entangling gates like CZ are likely to have lower fidelities d…
Colouring t-perfect graphs
Maria Chudnovsky, Linda Cook, James Davies +2
Perfect graphs can be described as the graphs whose stable set polytopes are defined by their non-negativity and clique inequalities (including edge inequalities). In 1975, Chváta…
On high genus extensions of Negami's conjecture
Marcin BriaÅski, James Davies, Jane Tan
Negami's famous planar cover conjecture is equivalent to the statement that a connected graph can be embedded in the projective plane if and only if it has a projective planar cove…