The creation and growth of components of a given complexity in a random graph process are studied. In particular, the expected number and total size of all such components is found...
We prove that the threshold for a random graph to have a k-core is equal to the threshold for having a subgraph which meets a necessary condition of Gallai for being k-critical. 1...
We present a linear expected time algorithm for finding maximum cardinality matchings in sparse random graphs. This is optimal and improves on previous results by a logarithmic f...
We prove that if T is a tree on n vertices with maximum degree and the edge probability p(n) satisfies: np C max{ log n, n } for some constant > 0, then with high probability...
In this work, we present a common framework for seeded image segmentation algorithms that yields two of the leading methods as special cases - The Graph Cuts and the Random Walker...