For a tree T and an integer k ≥ 1, it is well known that the k-th power T k of T is strongly chordal and hence has a strong elimination ordering of its vertices. In this note we...
Let G be a minimally k-connected graph with n nodes and m edges. Mader proved that if n 3k - 2 then m k(n - k), and for n 3k - 1 an equality is possible if, and only if, G is t...
The sum of a coloring is the sum of the colors assigned to the vertices (assuming that the colors are positive integers). The sum (G) of graph G is the smallest sum that can be ach...
We consider the following question: how large does n have to be to guarantee that in any two-colouring of the edges of the complete graph Kn,n there is a monochromatic Kk,k? In th...
Bounded Model Checking (BMC) searches for counterexamples to a property with a bounded length k. If no such counterexample is found, k is increased. This process terminates when ...