| タイトル | Hamiltonian Properties of Polyhedra |
|---|---|
| 開催日時 | 2017年1月23日 16:30～ |
| 主催者 | |
| 講演者 | Carol Zamfirescu 氏(Ghent University, Belgium) |
| 場所 | 矢上キャンパス14-631B |
| 内容 | In this talk we will discuss several related problems concerning hamiltonian properties of planar 3-connected graphs, which we will call polyhedra. The presentation will be divided intofour parts, with emphasis on new results, the techniques behind them, and open research problems. The first topic deals with 3-(vertex-)cuts in polyhedra, where we present a strengthening of the classic theorem of Tutte that 4-connected polyhedra are hamiltonian (joint work with Gunnar Brinkmann). This result also strengthens a theorem of Jackson and Yu on triangulations. In order toprovide context, we end this first part by giving an overview of results on hamiltonian properties of polyhedra with few 3-cuts (based on joint work with Kenta Ozeki and Nico Van Cleemput). In the second part of the talk, we present a geometrically motivated generalisation of Halin graphs, and study the hamiltonian properties of this family of polyhedra. We strengthen a result of Bondy. This is based on joint work with Boris Schauerte and Tudor Zamfirescu. The third topic concerns new bounds for the orders of the smallest $k$-regular polyhedra, $k \in \{3,4,5\}$, which are non-hamiltonian or non-traceable. We improve bounds of Zaks and Owens. This is joint work with Nico Van Cleemput. The talk ends with a study of 3-fragments (and in consequence cubic vertices) in planar hypohamiltonian graphs (which are necessarily 3-connected, and thus polyhedra). If time permits, more details -- such as sketches of proofs -- will be given for each of the above topics. |
| 資料 | |
| URL | http://www.comb.math.keio.ac.jp/seminar/index.html |
