The 'bisection width' of a graph is defined as the minumum number of edges that need to be removed to partition the graph into two equal halves. If the graph is 'sparse', then we don't expect this quantity to be large.
Insurance transfers losses associated with risks to the insurer for a price, the premium. We adopt the collective risk approach. Namely, we abstract the problem to include just two agents: the insured and the insurer.
We explore the visibility graph of a point set. We list some classical works on configurations of points and straight lines on the plain and then proceed to deduce some combinatorial properties of point visibility graphs.
A graph is $r$-regular if all its vertices have the same degree $r$. A random $r$-regular graph with $n$ vertices is a graph sampled uniformly at random from the set of all $r$-regular graphs on $n$ vertices.
Recent years have seen significant progress on the algorithmic aspects of the Lovasz Local Lemma: e.g., one can now handle super-polynomially many events that need to be avoided.
