Book embedding of graphs on surfaces based on cycle finding problems

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04975
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Yokohama National University
• Principal Investigator: Nakamoto Atsuhiro 横浜国立大学, 大学院環境情報研究院, 教授 (20314445)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: グラフ / 曲面 / 本型埋め込み / ページ数

Outline of Final Research Achievements

For a given graph, determining the page number seems to be a very important problem in both theoretical and practical reasons. In this research, our goal is to describe a relation between genus and page number of graphs, and we have succeeded in giving an upper bound for the page number of a graph embeddable on a surface, finding a suitable cycle of a graph with a good property. In particular, we have been able to give an upper bound for the page number of locally planar graphs on any orientable surfaces, and that for projective-planar graphs with respect to their connectivity.

Free Research Field

離散数学，グラフ理論