1-Embeddings on closed surfaces from the viewpoint of re-embeddings

2015 Fiscal Year Final Research Report

• Project/Area Number: 24740056
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Niigata University
• Principal Investigator: Suzuki Yusuke 新潟大学, 自然科学系, 准教授 (10390402)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 1-平面グラフ / 1-交差埋め込み / 閉曲面 / 三角形分割

Outline of Final Research Achievements

A graph is said to be 1-planar (or 1-embedding of a closed surface) if the graph can be drawn on the sphere (or the surface) so that each edge has at most one crossing point with another edge. In this research, we discuss 1-planar graphs (or 1-embeddings of closed surfaces) from the viewpoint of “re-embeddings”of those graphs, and obtained some results around this topic, which are clearly different from past results. In particular, in the joint work with Prof. Eades in Australia, we had shown that the problem of testing maximal 1-planarity of a graph can be solved in linear time, if a rotation system is given. Furthermore, we could prove that there exists no optimal 1-planar graph which can triangulate a non-orientable surface.

Free Research Field

位相幾何学的グラフ理論