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- W4300985837 abstract "We consider the following graph modification problem. Let the input consist of a graph $G=(V,E)$, a weight function $wcolon Vcup Erightarrow mathbb{N}$, a cost function $ccolon Vcup Erightarrow mathbb{N}$ and a degree function $deltacolon Vrightarrow mathbb{N}_0$, together with three integers $k_v, k_e$ and $C$. The question is whether we can delete a set of vertices of total weight at most $k_v$ and a set of edges of total weight at most $k_e$ so that the total cost of the deleted elements is at most $C$ and every non-deleted vertex $v$ has degree $delta(v)$ in the resulting graph $G'$. We also consider the variant in which $G'$ must be connected. Both problems are known to be NP-complete and W[1]-hard when parameterized by $k_v+k_e$. We prove that, when restricted to planar graphs, they stay NP-complete but have polynomial kernels when parameterized by $k_v+k_e$." @default.
- W4300985837 created "2022-10-04" @default.
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- W4300985837 date "2015-08-11" @default.
- W4300985837 modified "2023-10-17" @default.
- W4300985837 title "Editing to a Planar Graph of Given Degrees" @default.
- W4300985837 doi "https://doi.org/10.48550/arxiv.1508.02773" @default.
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