The question of whether the characteristic polynomial of a simple graph is uniquely determined by the characteristic polynomials of its vertex-deleted subgraphs is one of the many...
We consider a class of routing problems on connected graphs G. Initially, each vertex v of G is occupied by a “pebble” which has a unique destination π(v) in G (so that π is...
A card of a graph G is a subgraph formed by deleting one vertex. The Reconstruction Conjecture states that each graph with at least three vertices is determined by its multiset of...
We consider the problem of online sublinear expander reconstruction and its relation to random walks in “noisy” expanders. Given access to an adjacency list representation of ...
In this paper we consider the problem of testing whether a graph is triangle-free, and more generally, whether it is H-free, for a fixed subgraph H. The algorithm should accept gr...
Noga Alon, Tali Kaufman, Michael Krivelevich, Dana...