Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices ...
Let G be a simple graph with n vertices and m edges. Let ω(G) and α(G) be the numbers of vertices of the largest clique and the largest independent set in G, respectively. In th...
We consider the minimum line covering problem: given a set S of n points in the plane, we want to find the smallest number l of straight lines needed to cover all n points in S. W...
Let P be a set of n points in Ê3 , not all in a common plane. We solve a problem of Scott (1970) by showing that the connecting lines of P assume at least 2n − 7 different dir...
A pseudo-Boolean function is a real-valued function defined on {0, 1}n . A k-bounded function is a pseudo-Boolean function that can be expressed as a sum of subfunctions each of w...