Supereulerian line graphs

As shown by the second author, the existence of a spanning connected even subgraph in the line graph L(G) of a graph G is equivalent to the existence of a special dominating even subgraph in G. Recently, Huang et al. (2020) [4] also give a characterization of a graph with a supereulerian line graph. In this paper, we consider non-supereulerian line graphs and give the structure of an essentially 2-edge-connected graph with non-supereulerian line graphs. Moreover, as applications, we give two sufficient conditions for a graph G to ensure that its line graph L(G) is supereulerian. We correct a flaw of Huang's characterization and give its shorter proof.