著者

小林 みどり 喜安 善市 中村 義作

出版者

静岡県立大学経営情報学部

雑誌

経営と情報 : 静岡県立大学・経営情報学部/学報 (ISSN:09188215)

巻号頁・発行日

vol.3, no.1, pp.33-38, 1991-03-01

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We construct new perfect one-factorizations of the complete graphs K_<12168> and K_<29792>.

著者

小林 みどり 武藤 伸明 喜安 善市 中村 義作

出版者

静岡県立大学

雑誌

経営と情報 : 静岡県立大学・経営情報学部/学報 (ISSN:09188215)

巻号頁・発行日

vol.13, no.1, pp.1-6, 2000-12-15

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Dudeney's round table problem was proposed about one hundred years 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. In this paper, another solution of Dudeney's round table problem is given when n=p+2, where p is an odd prime number such that 2 or -2 is a primitive root of GF(p). The method of constructing the solution is new.

著者

小林 みどり 武藤 伸明 喜安 善市 中村 義作

出版者

静岡県立大学

雑誌

経営と情報 : 静岡県立大学・経営情報学部/学報 (ISSN:09188215)

巻号頁・発行日

vol.11, no.1, pp.69-76, 1998-11-30

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A set of Hamilton cycles in the complete graph K_n is called a [double] Dudeney set, if every path of length two lies on exactly one [two] of the cycles. It has been conjectured that there is a Dudeney set for every complete graph. It is known that there exists a Dudeney set of K_n when n is even, but it is still unsettled when n is odd. In this paper, we define a black 1-factor and we show that if there exists a black 1-factor of K_n, we can construct a Dudeney set of K_<n+1>. Furthermore, we extend it to a double Dudeney set.

著者

小林 みどり 喜安 善市

出版者

静岡県立大学

雑誌

経営と情報 : 静岡県立大学・経営情報学部/学報 (ISSN:09188215)

巻号頁・発行日

vol.8, no.2, pp.13-32, 1996-03-31

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A set of Hamilton cycles in the complete graph on n vertices is called a Dudeney set, if every path of length two lies on exactly one of the cycles. It has been conjectured that there is a Dudeney set for every complete graph, but it is still unsettled. Furthermore, little is known about the numder of non -isomorphic Dudeney sets. In this paper, we construct non-isomorphic Dudeney sets using perfect 1-factorizations and determine the number of the Dudeney sets and the automorphism groups.

著者

小林 みどり 喜安 善市 中村 義作

出版者

静岡県立大学

雑誌

経営と情報 : 静岡県立大学・経営情報学部/学報 (ISSN:09188215)

巻号頁・発行日

vol.14, no.2, pp.31-36, 2002-03-25

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A double Dudeney set in Kn is a multiset of Hamilton cycles in K_n having the property that each 2-path in K_n lies on exactly two of the cycles. In this paper, we construct a double Dudeney set in K_n when n=p^2+2, where p is an odd prime number.

著者

小林 みどり 喜安 善市 中村 義作

出版者

静岡県立大学

雑誌

経営と情報 : 静岡県立大学・経営情報学部/学報 (ISSN:09188215)

巻号頁・発行日

vol.3, no.1, pp.33-38, 1991-03

---

We construct new perfect one-factorizations of the complete graphs K_<12168> and K_<29792>.

著者

小林 みどり 喜安 善市 林田 侃

出版者

静岡県立大学

雑誌

経営と情報 : 静岡県立大学・経営情報学部/学報 (ISSN:09188215)

巻号頁・発行日

vol.9, no.2, pp.1-3, 1997-03-28

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A set of Hamilton cycles in the complete graph on n vertices is called a Dudeney set, if every path of length two lies on exactly one of the cycles. It has been conjectured that there is a Dudeney set for every complete graph, but it is still unsettled. Furthermore, little is known about the number of non-isomorphic Dudeney sets. In the previous paper, we constructed two types of new Dudeney sets using perfect 1-factorizations and determined the numbers of these Dudeney sets. In this paper, we show Dudeney sets of these types are not isomorphic, so the number of them are determined.