Motivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of \(K_1\cup P_4\) can act as a forbidden subgraph to ensure that every 1-tough H-free graph is hamiltonian, and that there is no other forbidden subgraph with this property, except possibly for the graph \(K_1\cup P_4\) itself. The hamiltonicity of 1-tough \(K_1\cup P_4\)-free graphs, as conjectured by Nikoghosyan, was left there as an open case. In this paper, we consider the stronger property of pancyclicity under the same condition. We find that the results are completely analogous to the hamiltonian case: every graph H such that any 1-tough H-free graph is hamiltonian also ensures that every 1-tough H-free graph is pancyclic, except for a few specific classes of graphs. Moreover, there is no other forbidden subgraph having this property. With respect to the open case for hamiltonicity of 1-tough \(K_1\cup P_4\)-free graphs we give infinite families of graphs that are not pancyclic.

受尼古霍斯扬（Nikogohosyan）的几个猜想的驱使，在最近由李（Li）等人撰写的一篇文章中，其目的是表征所有可能的图H，以使每个不含1韧度H的图都是哈密顿图。得出的结论几乎是完整的答案，即\（K_1 \ cup P_4 \）的每个适当的诱导子图H都可以充当禁止子图，以确保每个不含1的H无关图都是哈密顿图，并且没有具有此属性的其他禁止子图，但图\（K_1 \ cup P_4 \）本身可能除外。1韧性\（K_1 \ cup P_4 \）的咸味如Nikoghosyan猜想的那样，无图作为开放案例保留在那里。在本文中，我们考虑了在相同条件下泛环性的更强特性。我们发现结果与哈密顿情况完全相似：每个图H使得任何1韧H无图都是哈密顿图，还确保了每个1韧H无图都是全圈图，除了一些特定类别的图。此外，没有其他具有此属性的禁止子图。关于1韧度\（K_1 \ cup P_4 \） -无图的咸度的开放情况，我们给出了非泛环图的无穷图族。