A coloring is proper if each color class induces connected components of order one (where the order of a graph is its number of vertices). Here we study relaxations of proper two-c...
Let H be a fixed graph on h vertices. We say that a graph G is induced H-free if it does not contain any induced copy of H. Let G be a graph on n vertices and suppose that at leas...
We consider the vertex coloring problem, which may be stated as the problem of minimizing the number of labels that can be assigned to the vertices of a graph G such that each ver...
We study the topological simplification of graphs via random embeddings, leading ultimately to a reduction of the Gupta-Newman-Rabinovich-Sinclair (GNRS) L1 embedding conjecture t...
Large graph analysis has become increasingly important and is widely used in many applications such as web mining, social network analysis, biology, and information retrieval. The...