Online Node- and Edge-Deletion Problems with Advice

Abstract In online edge- and node-deletion problems the input arrives node by an algorithm has to delete nodes or edges in order keep graph a given class $$\Pi $$ Π at all times. We consider only hereditary properties , for which optimal algorithms exist can be characterized set of forbidden subgraphs $${{\mathcal{F}}}$$ F analyze advice complexity getting solution. give almost tight bounds on D elayed C onnected -N ode -D eletion P roblem where graphs family $${\mathcal{F}}$$ have connected lower upper $$H$$ H there is one induced subgraph H that may not. For basically easy function size biggest component . Additionally, we -E dge arbitrary number graphs. latter result present computes directly from separate analysis less general but admits bound easier compute.