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.

中文翻译：

---

具有匹配数和最小度约束的超欧拉图

如果图具有跨欧拉子图，则它是超欧拉图。我们证明，具有且仅当\（n = | V（G）| \ ge 2 \）和\（\ delta（G）\ ge \ alpha'（G）\）的连通简单图G是超欧拉式的。 ģ\ NE K_ {1，N-1} \）如果ñ是偶数还是\（G \ NE K_ {2中，n-2} \）如果ñ为奇数。因此，每个具有\（\ delta（G）\ ge \ alpha'（G）\）的连接的简单图G均具有哈密顿线形图。