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...
We consider random walks on two classes of random graphs and explore the likely structure of the vacant set viz. the set of unvisited vertices. Let (t) be the subgraph induced by ...
The task of finding the largest subset of vertices of a graph that induces a planar subgraph is known as the Maximum Induced Planar Subgraph problem (MIPS). In this paper, some n...
The r-Regular Induced Subgraph problem asks, given a graph G and a nonnegative integer k, whether G contains an r-regular induced subgraph of size at least k, that is, an induced ...
Let G be a regular graph and H a subgraph on the same vertex set. We give surprisingly compact formulas for the number of copies of H one expects to find in a random subgraph of G...