Editing to Eulerian graphs |
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Affiliation: | 1. School of Engineering and Computing Sciences, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom;2. Department of Informatics, University of Bergen, PB 7803, 5020 Bergen, Norway |
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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. |
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Keywords: | Eulerian graphs Graph editing Polynomial algorithm |
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