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- Igor Fabrici, Frank Göring
- Discussiones Mathematicae Graph Theory
- 2016

- Frank Göring, Christoph Helmberg, Markus Wappler
- SIAM Journal on Optimization
- 2008

We study the problem of maximizing the second smallest eigenvalue of the Laplace matrix of a graph over all nonnegative edge weightings with bounded total weight. The optimal value is the absolute algebraic connectivity introduced by Fiedler, who proved tight connections of this value to the connectivity of the graph. Using semidef-inite programming… (More)

- Thomas Böhme, Frank Göring, Jochen Harant
- Journal of Graph Theory
- 2001

Menger's Theorem for digraphs states that for any two vertex sets A and B of a digraph D such that A cannot be separated from B by a set of at most t vertices, there are t + 1 disjoint A-B-paths in D. Here a short and elementary proof of a more general theorem is given. For terminology and notation not deened here we refer to 1]. Recall that for a directed… (More)

- Frank Göring
- Discrete Mathematics
- 2000

A short proof of the classical theorem of Menger concerning the number of disjoint AB-paths of a nite digraph for two subsets A and B of its vertex set is given. c © 2000 Elsevier Science B.V. All rights reserved. MSC: 05C40

- Frank Göring, Jochen Harant, Dieter Rautenbach, Ingo Schiermeyer
- Discussiones Mathematicae Graph Theory
- 2009

Let F be a set of graphs and for a graph G let α F (G) and α * F (G) denote the maximum order of an induced subgraph of G which does not contain a graph in F as a subgraph and which does not contain a graph in F as an induced subgraph, respectively. Lower bounds on α F (G) and α * F (G) and algorithms realizing them are presented.

- Frank Göring, Christoph Helmberg, Markus Wappler
- Journal of Graph Theory
- 2006

Given a connected graph G = (N, E) with node weights s ∈ R N + and nonnegative edge lengths, we study the following embedding problem related to an eigenvalue optimization problem over the second smallest eigenvalue of the (scaled) Laplacian of G: Find vi ∈ R |N| , i ∈ N so that distances between adjacent nodes do not exceed prescribed edge lengths, the… (More)

- Tobias Gerlach, Frank Göring, Jochen Harant, Michal Tkác
- Discrete Mathematics
- 2006

For a set X of vertices of a graph fulfilling local connectedness conditions the existence of a cycle containing X is proved.

- Frank Göring, Jochen Harant, Erhard Hexel, Zsolt Tuza
- Discrete Mathematics
- 2004

For c 2 and k minfc; 3g, guaranteed upper bounds on the length of a shortest cycle through k prescribed vertices of a c-connected graph are proved. Analogous results on planar graphs are presented, too.

- Frank Göring, Christoph Helmberg, Susanna Reiss
- Math. Program.
- 2012

In analogy to the absolute algebraic connectivity of Fiedler, we study the problem of minimizing the maximum eigenvalue of the Laplacian of a graph by redistributing the edge weights. Via semidefinite duality this leads to a graph realization problem in which nodes should be placed as close as possible to the origin while adjacent nodes must keep a distance… (More)

- Piotr Borowiecki, Frank Göring, Jochen Harant, Dieter Rautenbach
- Journal of Graph Theory
- 2012

The well-known lower bound on the independence number of a graph due 1981) can be established as a performance guarantee of two natural and simple greedy algorithms or of a simple randomized algorithm. We study possible generalizations and improvements of these approaches using vertex weights and discuss conditions on so-called potential functions p G : V… (More)