Strongly sublinear separators and bounded asymptotic dimension for sphere intersection graphs

The  sphere dimension of a graph G is the smallest integer d≥2 so that G is an intersection graph of metric spheres in ℝ^d.

This talk considers the class C^d  of graphs with sphere dimension d.
We present the results that for each integer t, the class of all graphs in C^d that exclude K_t,t as a subgraph has strongly sublinear separators and that C^d has asymptotic dimension at most 2d+2.
 

The presented work is joined with James Davies, Agelos Georgakopoulos and Rose McCarty.