Spanning Eulerian subgraphs of bounded degree in triangulations (Q1334938)

A closed \(k\)-trail is a spanning Eulerian subgraph with maximum degree at most \(2k\). The main result states that every triangulation of a disk or an annulus has a closed 4-trail. Since every triangulation in the projective plane, the torus and the Klein bottle has a spanning subgraph which triangulates an annulus, this implies that all triangulations in the projective plane, the torus and the Klein bottle have closed 4- trails. The same holds for 5-connected triangulations in the double-torus with representativity at least 6.