The well-known bidimensionality theory provides a method for designing fast, subexponentialtime parameterized algorithms for a vast number of NP-hard problems on sparse graph classes such as planar graphs, bounded genus graphs, or, more generally, graphs with a fixed excluded minor. However, in order to apply the bidimensionality framework the considered problem needs to fulfill a special densi...

A bicolorable STS(v) is a Steiner triple system whose vertices are colored in such way that every block receives precisely two colors. A k-bicoloring of a STS is a vertex coloring using each of k colors, and the feasible set Ω is a set of integers k for which k-bicolorings exist. In this paper, we study feasible sets of STS(v)s of all orders v < 50.

S. Lüders, R. Baldinger, D. Baumeister, K. Bösiger, R. Eichler, M. Feuerstack–Raible, C. Grab, S. Löchner, B. Meier, P. Robmann, B.A. Schmid, U. Stange, S. Steiner, U. Straumann, S. Streuli, K. Szeker P. Truöl Institute for Particle Physics, ETH Zurich, 5232 Villigen PSI, Switzerland ASIC–Laboratory, Kirchhoff–Institute for Physics, 69120 Heidelberg, Germany Physics Institute, University of Zur...

Since 1971, numerous parameterized algorithms for the Steiner tree problem have been published, first of which was introduced by Dreyfus and Wagner. However, up to today there is not a single parameterized algorithm for the two-stage stochastic Steiner tree problem. This problem is still practically important and deserves more attention. This document first presents an algorithm that has a wors...

The upper chromatic number χ(H) of a set system H is the maximum number of colours that can be assigned to the elements of the underlying set of H in such a way that each H ∈ H contains a monochromatic pair of elements. We prove that a Steiner Triple System of order v ≤ 2 − 1 has an upper chromatic number which is at most k. This bound is the best possible, and the extremal configurations attai...

A bipartite graph G(X, Y) whose vertex set is partitioned into X and Y a convex graph, if there an ordering of $$X=(x_1,\ldots ,x_m)$$ such that for all $$y \in Y$$ , $$N_G(y)$$ consecutive with respect to the X, G said have convexity X. k-star caterpillar tree collection stars each star having k vertices degree one roots are joined by path. For partitions Y, we associate on in its neighborhood...

In the design of wireless networks, techniques for improving energy efficiency and extending network lifetime have great importance, particularly for defense and civil/rescue applications where resupplying transmitters with new batteries is not feasible. In this paper we study a method for improving the lifetime of wireless networks by minimizing the length of the longest edge in the interconne...

We study global routing of multiterminal nets. We propose a new global router; each step consists of finding a tree, called Steiner min-max tree, that is, a Steiner tree with maximum-weight edge minimized (real vertices represent channels containing terminals of a net, Steiner vertices represent intermediate channels, and weights correspond to densities). We propose an effient algorithm for obt...