A generalization of a theorem of Nash-Williams

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 ...${}_{\mathrm{}}{}_{\mathrm{}}$${}_{\mathrm{}}{}_{\mathrm{}}$${}_{\mathrm{}}{}_{\mathrm{}}$${}_{\mathrm{}}{}_{\mathrm{}}$

We consider toughness conditions that guarantee the existence of a hamiltonian cycle in k-trees, a subclass of the class of chordal graphs. By a result of Chen et al. 18-tough chordal graphs are hamiltonian, and by a result of Bauer et al. there exist ...

The cyclability of a graph H, denoted by C(H), is the largest integer r such that H has a cycle through any r vertices. For a claw-free graph H, by Ryjáă ek (J Comb Theory Ser B 70:217---224, 1997) closure concept, there is a $$K_3$$K3-free graph G such ...