Supereulerian graphs and matchings

A graph G is called supereulerian if G has a spanning Eulerian subgraph. Let α ′ ( G ) be the maximum number of independent edges in the graph G . In this paper, we show that if G is a 2-edge-connected simple graph and α ′ ( G ) ≤ 2 , then G is supereulerian if and only if G is not K 2 , t for some odd number t .