Finding the largest clique in random graphs is a well known hard problem. It is known that a random graph G(n, 1/2) almost surely has a clique of size about 2 log n. A simple greed...
We consider the problem of finding a sparse set of edges containing the minimum spanning tree (MST) of a random subgraph of G with high probability. The two random models that we ...
: Let G be a graph on n vertices in which every induced subgraph on s = log3 n vertices has an independent set of size at least t = log n. What is the largest q = q(n) so that ever...
Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s, k)-polar if there exists a pa...
Tinaz Ekim, Nadimpalli V. R. Mahadev, Dominique de...
We consider the parameterized complexity of the following problem under the framework introduced by Downey and Fellows[4]: Given a graph G, an integer parameter k and a non-trivial...