30 citations · 53 across the 12 of their papers we have counts for
5 papers · 1 filter
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…