Supereulerian Graphs with Constraints on the Matching Number and Minimum Degree

Abstract

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