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Supereulerian Graphs with Constraints on the Matching Number and Minimum Degree
Graphs and Combinatorics ( IF 0.6 ) Pub Date : 2020-09-03 , DOI: 10.1007/s00373-020-02229-x
Mansour J. Algefari , Hong-Jian Lai

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\(n = | V(G)| \ ge 2 \)\(\ delta(G)\ ge \ alpha'(G)\)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。

更新日期:2020-09-03
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