Spanning closed trails in graphs (Q686147)

The main result says that a 2-edge-connected graph on \(n>95\) vertices and with \(k\) vertices of degree 2 either has a spanning closed trail or can be contracted to \(K_{2,c-2}\), where \(c\leq \max\{5,3+k\}\) is an odd number, whenever \(k< n/5-19\) and for every edge \(uv\) with \(d(u)+ d(v)\geq 2n/5-2\).