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Editing to Eulerian graphs.

Dabrowski, K.K. and Golovach, P.A. and van 't Hof, P. and Paulusma, D. (2016) 'Editing to Eulerian graphs.', Journal of computer and system sciences., 82 (2). pp. 213-228.


The Eulerian Editing problem asks, given a graph G and an integer k, whether G can be modified into an Eulerian graph using at most k edge additions and edge deletions. We show that this problem is polynomial-time solvable for both undirected and directed graphs. We generalize these results for problems with degree parity constraints and degree balance constraints, respectively. We also consider the variants where vertex deletions are permitted. Combined with known results, this leads to full complexity classifications for both undirected and directed graphs and for every subset of the three graph operations.

Item Type:Article
Keywords:Eulerian graphs, Graph editing, Polynomial algorithm.
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2015 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:11 October 2015
Date deposited:09 November 2015
Date of first online publication:11 November 2015
Date first made open access:11 November 2016

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