We introduce two variants of proper colorings with imposed partial ordering on the set of colors. One variant shows very close connections to some fundamental problems in graph the...
We provide polynomial time data reduction rules for Connected Dominating Set in planar graphs and analyze these to obtain a linear kernel for the planar Connected Dominating Set pr...
We give the first linear kernels for DOMINATING SET and CONNECTED DOMINATING SET problems on graphs excluding a fixed graph H as a minor. In other words, we give polynomial time...
Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, ...
Abstract. The problem of clustering data can be formulated as a graph partitioning problem. In this setting, spectral methods for obtaining optimal solutions have received a lot of...
Marcus Weber, Wasinee Rungsarityotin, Alexander Sc...
We describe an algorithm for clustering using a similarity graph. The algorithm (a) runs in O(n log3 n + m log n) time on graphs with n vertices and m edges, and (b) with high pro...