Graph editing to a given degree sequence

Golovach, P.A.; Mertzios, G.B.

Abstract

We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence where the aim is to obtain a graph with a given degree sequence σσ by at most k vertex or edge deletions and edge additions. We show that the problem is W[1]-hard when parameterized by k for any combination of the allowed editing operations. From the positive side, we show that the problem can be solved in time 2O(k(Δ+k)2)n2logn2O(k(Δ+k)2)n2log⁡n for n-vertex graphs, where Δ=maxσΔ=maxσ, i.e., the problem is FPT when parameterized by k+Δk+Δ. We also show that Editing to a Graph with a Given Degree Sequence has a polynomial kernel when parameterized by k+Δk+Δ if only edge additions are allowed, and there is no polynomial kernel unless NP⊆coNP/polyNP⊆coNP/poly for all other combinations of allowed editing operations.

Citation

Golovach, P., & Mertzios, G. (2016, June). Graph editing to a given degree sequence. Presented at 11th International Computer Science Symposium in Russia., St. Petersburg, Russia

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 11th International Computer Science Symposium in Russia.
• Start Date: Jun 9, 2016
• End Date: Jun 13, 2016
• Acceptance Date: Feb 11, 2016
• Online Publication Date: May 31, 2016
• Publication Date: May 31, 2016
• Deposit Date: Feb 12, 2016
• Publicly Available Date: May 31, 2017
• Print ISSN: 0302-9743
• Pages: 177-191
• Series Title: Lecture notes in computer science
• Series Number: 9691
• Series ISSN: 0302-9743,1611-3349
• Book Title: Computer science – Theory and applications : 11th International Computer Science Symposium in Russia, CSR 2016, St. Petersburg, Russia, June 9-13, 2016. Proceedings.
• ISBN: 9783319341705
• DOI: https://doi.org/10.1007/978-3-319-34171-2_13
• Public URL: https://durham-repository.worktribe.com/output/1151029
• Additional Information: Conference Date: 9-13 June 2016