It is shown that if a d-dimensional cube is decomposed into n cubes, the side lengths of which belong to the interval (1 - n1/d+1; 1], then n is a perfect d-th power and all cubes are of the same size. This result is essentially tight. ...
2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...
We consider the problem of listing faces of the Minkowski sum of several V-polytopes in R^d. An algorithm for listing all faces of dimension up to j is presented, for any given 0
In this thesis we focus our attention on the stable set polytope of claw-free graphs. This problem has been open for many years and albeit all the efforts engaged during those last three years, it is still open. This does not mean that no progress has been ...