2-factors in 32\frac{3}{2}-tough plane triangulations

In 1956, Tutte proved the celebrated theorem that every 4-connected planar graph is hamiltonian. This result implies that every more than $\frac{3}{2}$-tough planar graph on at least three vertices is hamiltonian and so has a 2-factor. Owens in 1999 constructed non-hamiltonian maximal planar graphs of toughness arbitrarily close to $\frac{3}{2}$. In fact, the graphs Owens constructed do not even contain a 2-factor. Thus the toughness of exactly $\frac{3}{2}$ is the only case left in asking the existence of 2-factors in tough planar graphs. This question was also asked by Bauer, Broersma, and Schmeichel in a survey. In this paper, we close this gap by showing that every maximal $\frac{3}{2}$-tough planar graph on at least three vertices has a 2-factor

On some intriguing problems in Hamiltonian graph theory -- A survey

We survey results and open problems in Hamiltonian graph theory centred around three themes: regular graphs, $t$-tough graphs, and claw-free graphs

Stability number and f-factors in graphs

We present a new sufficient condition on stability number and toughness of the graph to have an f-factor