The Hamiltonicity of 4-connected graphs on the torus
Project/Area Number |
25871053
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Foundations of mathematics/Applied mathematics
Theory of informatics
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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
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Project Status |
Completed (Fiscal Year 2016)
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Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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Keywords | ハミルトン閉路 / Tutte 閉路 / タフネス / Hamilton 閉路 / 辺支配的部分グラフ / 完全マッチング / 頂点彩色 / Hamiltonian 閉路 / トーラス上のグラフ / 全域木 / Hamiltonian cycles / Tutte cycles / Graphs on surfaces / Claw-free graphs / Toughness / Forbidden subgraphs |
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.
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Report
(5 results)
Research Products
(77 results)
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[Presentation] Decomposition of plane cubic graphs2016
Author(s)
K. Ozeki
Organizer
The 4th Japan-Taiwan Conference on Combinatorics and its Applications
Place of Presentation
Kitakyushu International Conference Center, Kitakyushu (Japan)
Year and Date
2016-03-06
Related Report
Int'l Joint Research
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[Presentation] A HIST in cubic graphs2015
Author(s)
K. Ozeki
Organizer
8th Workshop on the Matthews-Sumner Conjecture and Related Problems
Place of Presentation
Hotel Trend, Pilsen (Czech Rebuplic)
Year and Date
2015-04-02
Related Report
Int'l Joint Research
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[Presentation] Decomposition of cubic graphs,2014
Author(s)
K. Ozeki
Organizer
ACCOTA 2014 - International Workshop Combinatorial and Computational Aspects of Optimization, Topology and Algebra
Place of Presentation
Ixtapa-Zihuatanejo (Mexico)
Year and Date
2014-11-25
Related Report
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