Supereulerian graphs and the Petersen graph (Q5917747)

A graph \(G\) is called supereulerian if \(G\) has a spanning closed trail. Using a reduction technique, which was developed by the first author [A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12, No. 1, 29-45 (1988; Zbl 0659.05073)], the authors prove that any 3-edge-connected graph with at most 10 edge cuts of size 3 either is a supereulerian graph or it is contractible to the Petersen graph.