We use the generalization of the Laplacian matrix to hypergraphs to obtain several spectral-like results on partition problems in hypergraphs which are computationally difficult to solve (NP-hard or NP-complete). Therefore it is very important to obtain nontrivial bounds. More precisely, the following parameters are bounded in the paper: bipartition width, averaged minimal cut, isoperimetric nu...

We investigate the parameterized complexity of Maximum Independent Set and Dominating Set restricted to certain geometric graphs. We show that Dominating Set is W[1]-hard for the intersection graphs of unit squares, unit disks, and line segments. For Maximum Independent Set, we show that the problem is W[1]-complete for unit segments, but fixed-parameter tractable if the segments are axis-paral...

For a given graph the maximum independent set problem is to find a maximum subset of vertices no two of which are adjacent. We propose a heuristic for the maximum independent set problem which utilizes classical results for the problem of optimization of a quadratic function over a sphere. The efficiency of the approach is confirmed by results of numerical experiments on DIMACS benchmarks.