Editing to Eulerian graphs

Dabrowski, K.K.; Golovach, P.A.; van 't Hof, P.; Paulusma, D.

Abstract

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.

Citation

Dabrowski, K., Golovach, P., van 't Hof, P., & Paulusma, D. (2016). Editing to Eulerian graphs. Journal of Computer and System Sciences, 82(2), 213-228. https://doi.org/10.1016/j.jcss.2015.10.003

• Journal Article Type: Article
• Acceptance Date: Oct 11, 2015
• Online Publication Date: Nov 11, 2015
• Publication Date: Mar 1, 2016
• Deposit Date: Nov 2, 2015
• Publicly Available Date: Nov 11, 2016
• Journal: Journal of Computer and System Sciences
• Print ISSN: 0022-0000
• Electronic ISSN: 1090-2724
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 82
• Issue: 2
• Pages: 213-228
• DOI: https://doi.org/10.1016/j.jcss.2015.10.003
• Keywords: Eulerian graphs, Graph editing, Polynomial algorithm.
• Public URL: https://durham-repository.worktribe.com/output/1396242