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We say a graph $G$ has a Hamiltonian path if it has a path containing allvertices of $G$. For a graph $G$, let $\sigma_2(G)$ denote the minimum degreesum of two nonadjacent vertices of $G$; restrictions on $\sigma_2(G)$ are knownas Ore-type conditions. Given an integer $t\geq 5$, we prove that if aconnected graph $G$ on $n$ vertices satisfies $\sigma_2(G)>{t-3\over t-2}n$,then $G$ has either a Hamiltonian path or an induced subgraph isomorphic to$K_{1, t}$. Moreover, we characterize all $n$-vertex graphs $G$ where$\sigma_2(G)={t-3\over t-2}n$ and $G$ has neither a Hamiltonian path nor aninduced subgraph isomorphic to $K_{1, t}$. This is an analogue of a recentresult by Mom\`ege, who investigated the case when $t=4$.

A sharp Ore-type condition for a connected graph with no induced star to have a Hamiltonian path