The connected graph of degree sequence 3, 3, 3, 1, 1, 1 is called a net, and the vertices of degree 1 in a net are called its endvertices. Broersma conjectured in 1993 that a 2-connected graph G with no induced \(K_{1,3}\) is hamiltonian if every endvertex of each induced net of G has degree at least \((|V(G)|-2)/3\). In this paper we prove this conjecture in the affirmative.

中文翻译：

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无爪图的感生网和汉密尔顿性

度数顺序为3、3、3、1、1、1的连通图称为网，而度数为1的顶点称为网的端点。Broersma于1993年推测，如果G的每个诱导网的每个顶点的度数至少为\（（||（V | G）| -2 ），则没有诱导\（K_ {1,3} \）的2连通图G是哈密顿量。）/ 3 \）。在本文中，我们肯定地证明了这一猜想。