The open webinar-- Many quartic vertices and short longest cycles in prisms over 3-polytopes
主 讲 人 ：Carol T. Zamfirescu
地 点 ：钉钉群
We shall discuss certainstructural properties of the Cartesian product of the 1-skeleton of a 3-polytopewith K2, i.e. its prism. We will generally use graph-theoretical notation butframe our results
in polytopal terminology,since many problems were originally formulated thusly. When we here speak of ad-polytope (i.e. a d-dimensional polytope), we are always referring to its1-skeleton. We recall that 3-polytopes have been characterised by Steinitz andcoincide with planar 3-connected graphs, and that by a theorem of Balinski,every d-polytope is d-connected. In 1973, Rosenfeld and Barnette conjectured thatevery 3-polytope has a hamiltonian prism. Almost half a century later, Špacapandisproved this conjecture. However, in his counterexamples the maximum degreeincreases with the graphs’ order.In this talk we shall address this issue andpresent several strengthenings of Špacapan’s main theorem.
Carol T. Zamfirescu received his Diploma inMathematics from TU Dortmund (Germany) in 2015, and his Ph.D. from GhentUniversity (Belgium) in 2016, under the supervision of Prof. Dr. GunnarBrinkmann. Since 2016 he is an FWO Postdoc at Ghent University, and since 2018an Adjunct Research Fellow at Babes-Bolyai University（巴贝斯-波利埃大学） in Cluj-Napoca, Roumania. The speaker’s areas of expertise are GraphTheory and Combinatorial Geometry.