@article{HM16maximumweighted, author = {Harant, Jochen and Mohr, Samuel}, journal = {Discrete Mathematics}, number = {7}, pages = {1954--1959}, publisher = {Elsevier}, title = {Maximum weighted induced subgraphs}, volume = {339}, year = {2016}, doi = {10.1016/j.disc.2015.07.013}, biburl = {http://samuel-mohr.de/files/bib/1.bib}, abstract = {Let {$G$} be a finite, simple, undirected graph with vertex set {$V(G)$} and {$\mathcal{F}$} be a family of graphs. A subgraph of {$G$} is {$\mathcal{F}$}-free if it does not contain any graph of {$\mathcal{F}$} as induced subgraph. In this paper, we present lower bounds on the maximum weight {$w(H) = \sum_{i\in V(H)} w_i$} of an {$\mathcal{F}$}-free induced subgraph {$H$} of {$G$}, where {$w_i > 0$} denotes the weight of a vertex {$i\in V(G)$}.} }