… An induced subgraph of G is called to be F -free if it does not contain any induced subgraph
… Since a graph with more vertices than G cannot be an induced subgraph of G , we assume …

… The maximum induced bipartite subgraph problem is NP -complete for clique-separable …
used to efficiently find maximum-weight induced k -partite subgraphs via dynamic programming, …

… )\) such that the subgraph induced by \(V'\) is connected and has maximum total edge weight
(ie \(\… We call this the maximum weight connected \(k\)-induced subgraph (Mwcis) problem. If …

… consider maximum weighted induced acyclic subgraphs of planar directed graphs. If the
maximum … We show that for planar graphs with maximum degree four the same problem is NP-…

… of tasks, including finding a maximum-weight induced subgraph of treewidth less than \(k\) …
of potential maximal cliques. Further developments, tailored to solve the maximum weight …

… subgraph with maximum total weight in a node-weighted (di)… They defined the maximum-weight
connected graph problem … the connected subgraph of maximum weight consisting of …

… However, it has been proven only with the Max Weight Independent Set problem in mind,
so we need to adjust the argumentation using the notion of treedepth structures. …

… induced subgraphs, which in particular imply a PTAS for the problem of finding a largest
induced subgraph … These results suggest that in graphs of bounded induced matching treewidth, …

… will be working on various induced subgraphs of G with vertex weight inherited from w.
Somewhat abusing notation, we will keep w for the weight function in any induced subgraph of G. …

… subgraphs, we will investigate the problem of finding an F-free induced subgraph H of G of
maximum weight w… an induced subgraph H of G, we define the weight of S and H as w(S) = ∑ …