The H-free process, for some fixed graph H, is the random graph process defined by starting
with an empty graph on n vertices and then adding edges one at a time, chosen uniformly at …

Consider the following stochastic graph process. We begin with G0, the empty graph on n
vertices, and form Gi by adding a randomly chosen edge ei to Gi− 1 where ei is chosen …

The triangle‐free process begins with an empty graph on n vertices and iteratively adds
edges chosen uniformly at random subject to the constraint that no triangle is formed. We …

The triangle-free process begins with an empty graph on n vertices and iteratively adds
edges chosen uniformly at random subject to the constraint that no triangle is formed. We …

In this paper we present distributed property-testing algorithms for graph properties in the
CONGEST model, with emphasis on testing subgraph-freeness. Testing a graph property P …

In this paper, we study the large-scale structure of dense regular graphs. This involves the
notion of robust expansion, a recent concept which has already been used successfully to …

There are a variety of existing conditions for a degree sequence to be graphic. When a
degree sequence satisfies any of these conditions, there exists a graph that realizes the …

In the standard CONGEST model for distributed network computing, it is known that" global"
tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large …

Abstract Proofs of Bell-Kochen-Specker contextuality demonstrate that there exists sets of
projectors that cannot each be assigned either 0 or 1 such that each basis formed from them …

We give a sharp refinement of a result of Alon, Ben-Shimon and Krivelevich. This gives a
sufficient condition for a finite sequence of positive integers to be the vertex degree list of …