%0 Generic %1 batagelj2002generalized %A Batagelj, Vladimir %A Zaveršnik, Matjaž %D 2002 %K core generalized p-core %T Generalized Cores %U http://arxiv.org/abs/cs/0202039 %X Cores are, besides connectivity components, one among few concepts that provides us with efficient decompositions of large graphs and networks. In the paper a generalization of the notion of core of a graph based on vertex property function is presented. It is shown that for the local monotone vertex property functions the corresponding cores can be determined in $O(m \max (\Delta, łog n))$ time.