Monotone edge flips to an orientation of maximum edge-connectivity à la Nash-Williams

@inproceedings{Ito2022MonotoneEF,
  title={Monotone edge flips to an orientation of maximum edge-connectivity {\`a} la Nash-Williams},
  author={Takehiro Ito and Yuni Iwamasa and Naonori Kakimura and Naoyuki Kamiyama and Yusuke Kobayashi and Shun-ichi Maezawa and Yuta Nozaki and Yoshio Okamoto and Kenta Ozeki},
  booktitle={SODA},
  year={2022}
}
We initiate the study of k-edge-connected orientations of undirected graphs through edge flips for k ≥ 2. We prove that in every orientation of an undirected 2k-edge-connected graph, there exists a sequence of edges such that flipping their directions one by one does not decrease the edge-connectivity, and the final orientation is k-edge-connected. This yields an “edge-flip based” new proof of Nash-Williams’ theorem: an undirected graph G has a k-edge-connected orientation if and only if G is… 
1 Citations
Independent set reconfiguration on directed graphs
TLDR
A linear-time algorithm for the problem on directed graphs whose underlying undirected graphs are trees, which are called polytrees, and a characterization of yes-instances based on the existence of a certain set of directed paths, which admits an e-cient algorithm.

References

SHOWING 1-10 OF 29 REFERENCES
On the existence of k edge-disjoint 2-connected spanning subgraphs
Flip Distances Between Graph Orientations
TLDR
It is proved that deciding whether the flip distance between two $\alpha$-orientations of a planar graph $G$ is at most two is \NP-complete, and this also holds in the special case of perfect matchings, where flips involve alternating cycles.
Packing of rigid spanning subgraphs and spanning trees
Strongly 2-connected orientations of graphs
On the orientation of graphs and hypergraphs
An Algorithm for Minimum Cost Arc-Connectivity Orientations
TLDR
An algorithm that runs in O(k3n3+kn2m) time without using sophisticated data structures is described and an application of the algorithm to find a shortest dijoin in O (n2M) time, which matches the current best bound.
Two‐connected orientations of Eulerian graphs
TLDR
It is proved that every weakly four-connected Eulerian graph has a 2-connected eigenvalue and is a special case of a conjecture of A. Frank.
Configurations in Graphs of Large Minimum Degree, Connectivity, or Chromatic Number
Wagner [42] proved that a graph of large chromatic number contains a subgraph that can be contracted into a large complete graph. Modifying Wagner's proof, Dirac [lo] and Jung [17] proved that, for
...
...