| Project/Area Number |
12640102
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | IBARAKI UNIVERSITY |
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Principal Investigator |
KANO Mikio IBARAKI UNIVERSITY, FACULTY OF ENGINEERING, PROFESSOR, 工学部, 教授 (20099823)
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| Co-Investigator(Kenkyū-buntansha) |
KANEKO Atsushi KOGAKUIN UNIVERSITY, FACULTY OF ENGINEERING, ASSOCIATE PROFESSOR, 工学部, 助教授 (30255608)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2001: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | Geometric Graph / Geometry in the Plane / Graph Embedding / Balanced Partition / Perfect Partition / Graph Theory / 幾何的グラフ / 凸集合 / 直線埋め込み / 2色点集合の分割 |
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| Research Abstract |
We mainly research the following two topics, and also study some related topics in graph theory.
For given graph G and set S of points in the plane, we want to embed G onto S so that each edge of G is a straight line segment, and each vertex is a point in S. If possible, we want to find such a embedding without crossings, if it is impossible to embed G onto S without crossings, we want to find a embedding with a small number of crossings.
We obtained some results on this topics by using graph theorict method and balanced partition methods. There are still some interesting unsolved problems, our results developed this area.
Another research topic is balanced partition problems. Namely, give a set of red points and a set of blue points in the plane, we want to divide the plane into k disjoint convex subsets so that each subset contains n_1 red points and n_i×m blue points under the assumption that n_1 + ・・・n_k red points and m(n_1 + ・・・ + n_k) blue points are given. If n_1 =・・・ =n_k, then this problem was partially solved by us and complete solved by three groups of researchers. We obtained some more general and related results on this problem.
The above two problems have a relation ship, and we wrote a survey entitled "Discrete Geometry on Red and Blue Points in the Plane - A Survey", which includes the above two topics as main parts. So these research area are new research area but becomes popular very fast.
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