Toughness, Forbidden Subgraphs and Pancyclicity

Abstract Motivated by several conjectures due to Nikoghosyan, in a recent article Li et al., the aim was characterize all possible graphs H such that every 1-tough -free graph is hamiltonian. The almost complete answer given there conclusion proper induced subgraph of $$K_1\cup P_4$$ K 1 ∪ P 4 can act as forbidden ensure hamiltonian, and no other with this property, except possibly for itself. hamiltonicity graphs, conjectured left an open case. In paper, we consider stronger property pancyclicity under same condition. We find results are completely analogous hamiltonian case: any also ensures pancyclic, few specific classes graphs. Moreover, having property. With respect case give infinite families not pancyclic.