LAUSR

A graph is supereulerian if it has a spanning eulerian subgraph. We show that a connected simple graph G with $$n = |V(G)| \ge 2$$ n = | V ( G ) | ≥ 2 and $$\delta (G) \ge \alpha '(G)$$ δ ( G ) ≥ α ′ ( G ) is supereulerian if and only if $$G \ne K_{1,n-1}$$ G ≠ K 1 , n - 1 if n is even or $$G \ne K_{2, n-2}$$ G ≠ K 2 , n - 2 if n is odd. Consequently, every connected simple graph G with $$\delta (G) \ge \alpha '(G)$$ δ ( G ) ≥ α ′ ( G ) has a hamiltonian line graph.