Abstract
A graph is supereulerian if it has a spanning eulerian subgraph. We show that a connected simple graph G with n=vertical bar V(G)vertical bar >= 2 and delta(G)>=alpha '(G) is supereulerian if and only if G not equal K-1,K-n-1 if n is even or G not equal K-2,K-n-2 if n is odd. Consequently, every connected simple graph G with delta(G) >= alpha '(G) has a hamiltonian line graph.