4 problems

A greedy drawing of a graph $G$ is a Euclidean drawing in which, for every pair of distinct vertices $s,t$, the vertex $s$ has a neighbor $u$ satisfying $d(s,t)>d(u,t)$, where $d$…

Continuous-circle greedy-routing conjecture. For every $\varepsilon>0$, there exists a constant $K_0=K_0(\varepsilon)$ such that, for all $K\geq K_0$ and sufficiently large $n$, wi…

Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be two families of graphs with bounded doubling dimension, not necessarily with the same constants. For any two graphs…

A double clustering graph is constructed from two graphs on a common vertex set by applying a random permutation to one graph and adding an edge $(u,v)$ whenever every vertex close…