Research on similarities and dissimilarities between the blocking and anti-blocking polyhedra
| 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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Report
(6 results)
Research Products
(27 results)
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[Journal Article] Safe sets in graphs: Graph classes and structural parameters2018
Author(s)
Raquel Agueda, Nathann Cohen, Shinya Fujita, Sylvain Legay, Yannis Manoussakis, Yasuko Matsui, Leandro Montero, Reza Naserasr, Hirotaka Ono, Yota Otachi, Tadashi Sakuma, Zsolt Tuza, Renyu Xu
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Journal Title
Journal of Combinatorial Optimization
Volume: 印刷中
Issue: 4
Pages: 1221-1242
DOI
Related Report
Peer Reviewed / Int'l Joint Research
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