An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero, and it is well known that a graph has exactly one ma...
A spanning tree T in a finite planar connected graph G determines a dual spanning tree T in the dual graph G such that T and T do not intersect. We show that it is not always poss...
A graph is called biclaw-free if it has no biclaw as an induced subgraph. In this note, we prove that if G is a connected bipartite biclaw-free graph with (G) 5, then G is collap...
For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connect...
Referring to the query complexity of property testing, we prove the existence of a rich hierarchy of corresponding complexity classes. That is, for any relevant function q, we prov...
Oded Goldreich, Michael Krivelevich, Ilan Newman, ...