—We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of bounded-degree graphs wit...
Avinatan Hassidim, Jonathan A. Kelner, Huy N. Nguy...
We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − )n vertices, in terms of the expansion prop...
Given a class of graphs F, we say that a graph G is universal for F, or F-universal, if every H ∈ F is contained in G as a subgraph. The construction of sparse universal graphs ...
Daniel Johannsen, Michael Krivelevich, Wojciech Sa...
A large body of work has been devoted to identifying community structure in networks. A community is often though of as a set of nodes that has more connections between its member...
Jure Leskovec, Kevin J. Lang, Anirban Dasgupta, Mi...
We study the properties of embeddings, multicommodity flows, and sparse cuts in minor-closed families of graphs which are also closed under 2-sums; this includes planar graphs, g...
Amit Chakrabarti, Alexander Jaffe, James R. Lee, J...