2001 Fiscal Year Final Research Report Summary
| Project/Area Number |
11640131
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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 | University of Shizuoka |
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Principal Investigator |
KOBAYASHI Midori University of Shizuoka, School of Administration and Informal, Professor, 経営情報学部, 教授 (00136631)
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| Project Period (FY) |
1999 – 2001
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| Keywords | neighbor design / Hamilton cycle / 1-factorization / dudeney set |
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| Research Abstract |
Dudeney's round table problem was proposed about one hundred year, ago. It is already solved when the number of people is even, but it is still unsettled except only few cases when the number of people is odd.
1. In this research, a solution of Dudeney's round table problem is given when n = p + 2, where p is an odd prime number such that -2 is a primitive root of GF(p), or 2 is the square of a primitive root of GF(p) and p≡3 (mod 4).
2. A double Dudeney set in K_n is a multiset of Hamilton cycles having the property that each 2-path lies in exactly two of the cycles. A double Dudeney set in K_n has been constructed when n is even. In this research, we constructed a double Dudeney set in K_n when n is odd.
3.Some classes of 1-factorizations of complete grahs are known. In this research, infinite kinds of new 1-factorizations of complete graphs are given.
4. Dudeney's round table problem is the problem of contructing a uniform covering of 2-paths by hamilton cyles. In this research, we constructed a uniform covering of 2-paths by 4-paths and a uniform covering of 2-paths by 5-paths.
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