| Project/Area Number |
18K03388
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12030:Basic mathematics-related
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| Research Institution | Yamagata University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 期待到達時間 / フィボナッチ数列 / Tutte多項式 / Pebble motion problem / safe set problem / Packing and Covering / average hitting time / Fibonacci number / pebble motion problem / safe number / FPTAS / Tutte Polynomial / safe set / tute polynomial / network majority / 凸幾何 / connected safe set / lattice / グラフの自己同型群 / 石交換群 / tutte polynomial / gold grabbing game / convex geometry / weighted safe set / Anti-Blocking型整数多面体 / Blocking型の整数多面体 / ideal clutter / perfect graph / Ideal Clutter / Perfect Graph / the MFMC property / パッキングとカバリングの理論 |
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| Outline of Final Research Achievements |
Proved a beautiful relationship between the expected arrival time of the squared graph of cycles and the Fibonacci number, generalizing the Tutte polynomial and the Pebble Motion Problem; overturned Ehard & Rautenbach's conjecture of connected safe set minimization in point weighted trees Showed that the problem belongs to FPTAS, solving one of the open problems of Tittmann et al [Eur J Combin 32, 2011]; partial solution of a conjecture of Cornuejols, Guenin and Margot; first in the world to show that the Tutte polynomial problem belongs to FPTAS. Gives, for the first time in the world, a combinatorial interpretation for the Tutte polynomial at (x, y) = (2, -1).
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| Academic Significance and Societal Importance of the Research Achievements |
離散数学の幅広い分野において（期待到達時間、Tutte多項式、Pebble Motion Problem、Safe Set Problem、Clutter Packing and Covering Problemなど）に対し、複数の未解決問題を解決し、既存の枠組みの一般化を行った。特筆すべき結果としては、世界で初めて Tutte polynomialの(x, y) = (2, －1)における値に組合せ論的解釈を与えたことなどが挙げられる。
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