A new result on local forbidden graph and hamiltonicity (Q1913915)

Let \(G= (V, E)\) be a graph of order \(n\), \(V_0= \{v\in V\mid \deg(v)\geq {n\over 2}\}\), \(\overline V_0= V\backslash V_0\), \(G[\overline V_0]\) the subgraph of \(G\) induced by the vertices of \(\overline V_0\) and \(F\) the unique graph with degree sequence 333111 (often also denoted by \(N\) and referred to as the net). The following conjecture by Zhu is proved. If \(G\) is a 3-connected graph such that \(G[\overline V_0]\) contains no induced subgraph \(F\) and each induced subgraph \(K_{1, 3}\) of \(G\) has at least one endvertex in \(V_0\), then \(G\) is hamiltonian.