| Project/Area Number |
26400185
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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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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Yamagata University |
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Principal Investigator |
Sakuma Tadashi 山形大学, 地域教育文化学部, 准教授 (60323458)
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| Co-Investigator(Kenkyū-buntansha) |
柏原 賢二 東京大学, 大学院総合文化研究科, 助教 (70282514)
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| Co-Investigator(Renkei-kenkyūsha) |
HACHIMORI Masahiro 筑波大学, システム情報系, 准教授 (00344862)
NAKAMURA Masataka 東京大学, 大学院総合文化研究科, 准教授 (90155854)
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| Research Collaborator |
SHINOHARA Hidehiro
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | Ideal clutter / Packing Property / MFMC Property / Tutte Polynomial / Chord Diagram / safe set / network majority / Packing and Covering / weighted sefe set / ブロッキング型整数多面体 / アンチブロッキング型整数多面体 / パッキングとカバリングの理論 / クラッター / packing property / MFMC-性 / 理想グラフ / near factorization / packing and covering / blocking polyhedra / anti-blocking polytope / perfect graph / ideal cullter / MFMC-property / 巡回群 / ideal clutter |
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| Outline of Final Research Achievements |
1): We give a scheme to attack the following conjecture proposed by Cornuejols, Guenin and Margot:"Every ideal minimally non-packing clutter has a transversal of size 2." Moreover, we show that the clutter of a combinatorial affine plane does not have any ideal minimally non-packing clutter of blocking number at least 3. 2): We prove that the chord expansion number equals the value of the Tutte polynomial at the point (2,-1) for its corresponding interlace graph. 3): A safe set of a graph G=(V,E) is a non-empty subset S of V such that for every component A of G[S] and every component B of G[V-S], we have |A|+1>|B| whenever there exists an edge of G between A and B. We give several graph theoretical properties of this concept. Furthermore we evaluate computational complexities of the problem of computing the minimum weight of a safe set on several graph classes.
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