# On Making Directed Graphs Eulerian

@article{Sorge2011OnMD, title={On Making Directed Graphs Eulerian}, author={Manuel Sorge}, journal={ArXiv}, year={2011}, volume={abs/1101.4283} }

A directed graph is called Eulerian, if it contains a tour that traverses every arc in the graph exactly once. We study the problem of Eulerian extension (EE) where a directed multigraph G and a weight function is given and it is asked whether G can be made Eulerian by adding arcs whose total weight does not exceed a given threshold. This problem is motivated through applications in vehicle routing and flowshop scheduling. However, EE is NP-hard and thus we use the parameterized complexity…

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## 4 Citations

From Few Components to an Eulerian Graph by Adding Arcs

- MathematicsWG
- 2011

It is shown that EE is fixed-parameter tractable with respect to the combined parameter "number of connected components in the underlying undirected multigraph" and "sum of indeg - outdeg over all vertices v in the input multigraph where this value is positive".

Efficient Algorithms for Eulerian Extension and Rural Postman

- Computer ScienceSIAM J. Discret. Math.
- 2013

This work shows that the NP-hard Weighted Multigraph Eulerian Extension problem is fixed-parameter tractable with respect to the number of extension arcs, and presents several polynomial-time algorithms for natural Euleria extension problems, including undirected variants which can be defined analogously to the directed ones.

Parameterized Complexity of Eulerian Deletion Problems

- Computer ScienceAlgorithmica
- 2012

A randomized FPT algorithm for making an undirected graph Eulerian by deleting the minimum number of edges, based on a novel application of the color coding technique is shown, proving that this is not possible unless NP⊆coNP/poly.

A new view on Rural Postman based on Eulerian Extension and Matching

- MathematicsJ. Discrete Algorithms
- 2011

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