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

---

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.