Editing to a planar graph of given degrees

Konrad K. Dabrowski , Petr A. Golovach (1) , Pim van 'T Hof (2) , Daniël Paulusma (3) , Dimitrios M. Thilikos (4, 5)

1 School of Engineering and Computing Sciences
2 UiB - Department of Informatics [Bergen]
3 Department of Computer Science
4 Department of Mathematics [Athens]
5 ALGCO - Algorithmes, Graphes et Combinatoire

We consider the following graph modification problem. Let the input consist of a graph G = (V, E), a weight function w : V ∪E → N, a cost function c : V ∪ E → N and a degree function δ : V → N0, together with three integers kv, ke and C. The question is whether we can delete a set of vertices of total weight at most kv and a set of edges of total weight at most ke so that the total cost of the deleted elements is at most C and every non-deleted vertex v has degree δ(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 kv + ke. We prove that, when restricted to planar graphs, they stay NP-complete but have polynomial kernels when parameterized by kv + ke.

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]

Konrad K. Dabrowski, Petr A. Golovach, Pim van 'T Hof, Daniël Paulusma, Dimitrios M. Thilikos. Editing to a planar graph of given degrees. Journal of Computer and System Sciences, 2017, 85, pp.168-182. ⟨10.1016/j.jcss.2016.11.009⟩. ⟨hal-01632341⟩