Safe edge of a dual line arrangement
= Safe edge of a dual line arrangement
= Safe dual-arrangement edge
{synonym}
A <safe dual-arrangement edge> is one for which every edge on a path of length at most two from either endpoint is a <good dual-arrangement edge>. This stronger local condition supplies a two-cell-thick triangular strip. Only a bounded multiple of the original bad edges can be unsafe: trace a shortest path to the first bad edge and reverse it through degree-six intermediate vertices.