The Hamiltonicity of 4-connected graphs on the torus

2016 Fiscal Year Final Research Report

• Project/Area Number: 25871053
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics; Theory of informatics
• Research Institution: National Institute of Informatics
• Principal Investigator: Ozeki Kenta 国立情報学研究所, ビッグデータ数理国際研究センター, 特任助教 (10649122)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: ハミルトン閉路 / Tutte 閉路 / タフネス

Outline of Final Research Achievements

Since a well-known conjecture due to Grunbaum and Nash-Williams, the Hamiltonicity of 4-connected graphs on the torus has been attracted by many researchers. In this work, I have had attempt to solve this conjecture, and obtained several results.
For example, I posed ``to improve a known method, so-called Tutte cycle (or path)'' as one of the main target in this work. In fact, I have succeeded this and obtained some results using an improved Tutte cycle. I also gave some other results on the toughness of graphs, which I also posed when this work began.
I also obtained several other results, which have been presented as academic articles or talks in conferences.

Free Research Field

離散数学