A differential poset is a partially ordered set with raising and lowering operators U and D which satisfy the commutation relation DU-UD = rI for some constant r. This notion may ...
An old problem of Erd˝os, Fajtlowicz and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on n vertices. Motivated by this problem...
Michael Krivelevich, Benny Sudakov, Nicholas C. Wo...
An induced subgraph is called homogeneous if it is either a clique or an independent set. Let hom(G) denote the size of the largest homogeneous subgraph of a graph G. In this shor...
: In this paper, we study spectral versions of the densest subgraph problem and the largest independence subset problem. In the first part, we give an algorithm for identifying sm...
For a family F of graphs, a graph U is said to be F-universal if every graph of F is a subgraph of U. Similarly, a graph is said to be F-induced-universal if every graph of F is a...