A Parameterized Complexity View on Collapsing k-Cores

Abstract We study the -hard graph problem Collapsed k-Core where, given an undirected G and integers b , x k we are asked to remove vertices such that -core of remaining graph, is, (uniquely determined) largest induced subgraph with minimum degree has size at most . was introduced by Zhang et al. (2017) it is motivated engagement behavior users in a social network measuring resilience against user drop outs. generalization r-Degenerate Vertex Deletion (which known be for all r ≥ 0) -degenerate, every its investigate parameterized complexity respect parameters several structural input graph. reveal dichotomy computational ≤ 2 3. For latter case 0 when show ( + ). Furthermore, outline treewidth presumably does not admit polynomial kernel vertex cover number