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Durham University

Computer Science


Publication details for Dr George Mertzios

Golovach, P.A. & Mertzios, G.B. (2016), Graph editing to a given degree sequence, in Kulikov, A.S. & Woeginger, G. eds, Lecture Notes in Computer Science, 9691 11th International Computer Science Symposium in Russia. St. Petersburg, Russia, Springer, Cham, Switzerland, 177-191.

Author(s) from Durham


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.


Conference Date: 9-13 June 2016