what is the k-line-connected graph definition What is the definition for k-line-connectedness of the graph ? I am in doubt whether it differs from usual k-vertex (edge) connectedness. I've encountered it in the paper titled "Np-complete problems on a 3-connected cubic planar graph and their applications" where it comes without definition. Unfortunately for me I couldn't get the definition from the context given in its authors' proofs.
Judging from the proof of Lemma 1 in the paper, 3-line-connected is the same as 3-edge-connected; line is probably a translation from Japanese.