cs.DS

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Title: Editing to a Planar Graph of Given Degrees

Abstract: We consider the following graph modification problem. Let the input consist of a graph $G=(V,E)$, a weight function $w\colon V\cup E\rightarrow \mathbb{N}$, a cost function $c\colon V\cup E\rightarrow \mathbb{N}$ and a degree function $\delta\colon V\rightarrow \mathbb{N}_0$, 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 $k_v+k_e$.
 Subjects: Data Structures and Algorithms (cs.DS); Computational Complexity (cs.CC) Cite as: arXiv:1508.02773 [cs.DS] (or arXiv:1508.02773v1 [cs.DS] for this version)

Submission history

From: Daniel Paulusma [view email]
[v1] Tue, 11 Aug 2015 23:30:20 GMT (37kb)
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