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

  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},
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… 
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