Strongly sublinear separators and bounded asymptotic dimension for sphere intersection graphs
By: James Davies , Agelos Georgakopoulos , Meike Hatzel and more
Potential Business Impact:
Graphs with no repeating parts have simple structures.
In this paper, we consider the class $\mathcal{C}^d$ of sphere intersection graphs in $\mathbb{R}^d$ for $d \geq 2$. We show that for each integer $t$, the class of all graphs in $\mathcal{C}^d$ that exclude $K_{t,t}$ as a subgraph has strongly sublinear separators. We also prove that $\mathcal{C}^d$ has asymptotic dimension at most $2d+2$.
Similar Papers
On cuts of small chromatic number in sparse graphs
Combinatorics
Graphs can be split into smaller, easier parts.
Sparse Bounded Hop-Spanners for Geometric Intersection Graphs
Computational Geometry
Makes computer networks faster and more efficient.
Truly Subquadratic Time Algorithms for Diameter and Related Problems in Graphs of Bounded VC-dimension
Data Structures and Algorithms
Finds the longest distance in a network faster.