Fig. 17
From: Investigating the complexity of the double distance problems
(i) A cycle-line of length 4 or larger only allows plug connections. In contrast, cycle-lines of lengths 1–3 admit other types of connections (see Figs. 14 and A7, A8, the last two in Additional file 1). (ii) If the cycle-line has even length and plug connections at both sides, we have a balanced link: either the yellow or the green solution will be fixed later; it will be the one compatible with the selected independent set of the unsaturated path-line ending in \(u'\) concatenated to the one starting in \(v'\)