James Davies

activity

20192026

most citedCircle graphs are quadratically

χ

-bounded

30 citations · 53 across the 12 of their papers we have counts for

collaborators

Showing 2020Show all

3 papers · 1 filter

math.CO2020★ 4 cited

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 $R^{3}$ and intersection graphs of straight lines in $R^{3}$ that have arbitrarily large girth an…

math.CO2020★ 2 cited

Vertex-minor-closed classes are $χ$ -bounded

James Davies

We prove a conjecture of Geelen that every proper vertex-minor-closed class of graphs is $χ$ -bounded.

math.CO2020

Locally Hamiltonian graphs and minimal size of maximal graphs on a surface

James Davies, Carsten Thomassen

We prove that every locally Hamiltonian graph with $n \geq 3$ vertices and possibly with multiple edges has at least $3 n - 6$ edges with equality if and only if it triangulates the sph…

Box and segment intersection graphs with large girth and chromatic number

Vertex-minor-closed classes are χ-bounded

Locally Hamiltonian graphs and minimal size of maximal graphs on a surface

Vertex-minor-closed classes are $χ$ -bounded