Frank Göring

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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.
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)