Events
DMS Combinatorics Seminar 
Time: Mar 16, 2023 (02:00 PM) 
Location: 328 Parker Hall/ZOOM 
Details: Speaker: Songling Shan, Illinois State University/Auburn
Title: 2factors in 3/2tough plane triangulations Abstract: In 1956, Tutte proved the celebrated theorem that every 4connected 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 2factor. Owens in 1999 constructed nonhamiltonian maximal planar graphs of toughness smaller than $\frac{3}{2}$. In fact, the graphs Owens constructed do not even contain a 2factor. Thus the toughness of exactly $\frac{3}{2}$ is the only case left in asking about the existence of 2factors in tough planar graphs. This question was also asked by Bauer, Broersma, and Schmeichel in a survey. We close this gap by showing that every maximal $\frac{3}{2}$tough plane graph on at least three vertices has a 2factor.
