Let G be a simple graph with n vertices and m edges. Let ω(G) and α(G) be the numbers of vertices of the largest clique and the largest independent set in G, respectively. In th...
We examine the relationship of a graph G and its random subgraphs which are defined by independently choosing each edge with probability p. Suppose that G has a spectral gap λ (...
The class of graphs where the size of a minimum vertex cover equals that of a maximum matching is known as K¨onig-Egerv´ary graphs. K¨onig-Egerv´ary graphs have been studied ex...
In order to enable scalable querying of graph databases, intelligent selection of subgraphs to index is essential. An improved index can reduce response times for graph queries si...
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...