As many readers may know, graph theory is a fundamental branch of mathematics that
explores networks made up of nodes and edges, focusing on their paths, structures, and …

In this paper, we show that any n point metric space can be embedded into a distribution
over dominating tree metrics such that the expected stretch of any edge is O (log n). This …

We introduce a new framework for designing fixed-parameter algorithms with
subexponential running time---2 O (√ k) n O (1). Our results apply to a broad family of graph …

At the core of the seminal graph minor theory of Robertson and Seymour is a powerful
structural theorem capturing the structure of graphs excluding a fixed minor. This result is …

Motivated by many recent algorithmic applications, this paper aims to promote a systematic
study of the relationship between the topology of a graph and the metric distortion incurred …

Quantum networks will allow to implement communication tasks beyond the reach of their
classical counterparts. A pressing and necessary issue for the design of quantum network …

Graph sparsification aims at compressing large graphs into smaller ones while preserving
important characteristics of the input graph. In this work we study vertex sparsifiers, ie …

We solve an open problem posed by Eppstein in 1995 and re-enforced by Grohe
concerning locally bounded treewidth in minor-closed families of graphs. A graph has …

We introduce the following notion of compressing an undirected graph G with (nonnegative)
edge-lengths and terminal vertices R⊆V(G). A distance-preserving minor is a minor G' (of G) …

In this article, we study metrics of negative type, which are metrics (V, d) such that√ d is an
Euclidean metric; these metrics are thus also known as ℓ2-squared metrics. We show how to …