A cutting-plane approach to the edge-weighted maximal clique problem

We investigated the computational performance of a cutting-plane algorithm for the problem of determining a maximal subclique in an edge-weighted complete graph. Our numerical results are contrasted with reports on closely related problems for which cutting-plane approaches perform well in instances of moderate size. Somewhat surprisingly, we find that our approach already in the case of n = 15 or N = 25 nodes in the underlying graph typically neither produces an integral solution nor yields a good approximation to the true optimal objective function value. This result seems to shed some doubt on the universal applicability of cuttingplane approaches as an efficient means to solve linear (0, 1)-programming problems of moderate size

An efficient algorithm for nucleolus and prekernel computation in some classes of TU-games

We consider classes of TU-games. We show that we can efficiently compute an allocation in the intersection of the prekernel and the least core of the game if we can efficiently compute the minimum excess for any given allocation. In the case where the prekernel of the game contains exactly one core vector, our algorithm computes the nucleolus of the game. This generalizes both a recent result by Kuipers on the computation of the nucleolus for convex games and a classical result by Megiddo on the nucleolus of standard tree games to classes of more general minimum cost spanning tree games. Our algorithm is based on the ellipsoid method and Maschler's scheme for approximating the prekernel. \u

Note on the game chromatic index of trees

We study edge coloring games defining the so-called game chromatic index of a graph. It has been reported that the game chromatic index of trees with maximum degree $\Delta = 3$ is at most $\Delta + 1$. We show that the same holds true in case $\Delta \geq 6$, which would leave only the cases $\Delta = 4$ and $\Delta = 5$ open. \u

Some order dimension bounds for communication complexity problems

We associate with a general (0, 1)-matrixM an ordered setP(M) and derive lower and upper bounds for the deterministic communication complexity ofM in terms of the order dimension ofP(M). We furthermore consider the special class of communication matricesM obtained as cliques vs. stable sets incidence matrices of comparability graphsG. We bound their complexity byO((logd)·(logn)), wheren is the number of nodes ofG andd is the order dimension of an orientation ofG. In this special case, our bound is shown to improve other well-known bounds obtained for the general cliques vs. stable set problem

Cologne/Twente workshop on graphs and combinatorial optimization CTW 2007

The 6th Cologne-Twente Workshop on Graphs and Combinatorial Optimization (CTW 2007) was held at the University of Twente, The Netherlands, 29-31 May, 2007. The CTW started as a series of biennial meetings at the Universities of Cologne in Germany and Twente in the Netherlands. Ever increasing interest has turned the CTW into a now annual event with the Politecnico di Milano, the University of Duisburg-Essen, the Universit degli Studi di Milano, and Ecole Polytechnique in Paris as additional partners. The scope of the workshop comprises the theory and applications of discrete algorithms, graphs, and combinatorial structures in the wide sense. After the workshop, the participants and the research community at large were invited to submit research articles relating to the themes of the workshop. As guest editors, we are pleased to present a collection of articles that were selected from the submissions by the refereeing process. We thank all the contributors for making it so easy to document the workshop and the state-of-the-art with interesting articles and we hope that you, the reader, will find these contributions stimulating as well