Multiple Dudeney Sets

Search this Article

Author(s)

Abstract

A set of Hamilton cycles in the complete graph K_n is called a λ-ply Dudeney set if every path of length two lies on exactly λ of the cycles. The problem of constructing a λ-ply Dudeney set in Kn has been solved when n is even, but it is still open when n is odd. In this paper, we construct a λ-ply Dudeney set in Kn, where λ=n-3 when n=4k + 3 (k ≥ 1), and II^<e-1>_<i=0>(2^<e-i>k_1-2) when n=2^ek_1+1 ≥ 5 (e ≥ 1, k_1 is odd).

A set of Hamilton cycles in the complete graph K_n is called a λ-ply Dudeney set if every path of length two lies on exactly λ of the cycles. The problem of constructing a λ-ply Dudeney set in Kn has been solved when n is even, but it is still open when n is odd. In this paper, we construct a λ-ply Dudeney set in Kn, where λ=n-3 when n=4k + 3 (k ≥ 1), and II^<e-1>_<i=0>(2^<e-i>k_1-2) when n=2^ek_1+1 ≥ 5 (e ≥ 1, k_1 is odd).

Journal

Codes

  • NII Article ID (NAID)
    110006227311
  • NII NACSIS-CAT ID (NCID)
    AN10118525
  • Text Lang
    ENG
  • Article Type
    Departmental Bulletin Paper
  • Journal Type
    大学紀要
  • ISSN
    09188215
  • NDL Article ID
    6115697
  • NDL Source Classification
    ZF1(教育)
  • NDL Call No.
    Z7-3446
  • Data Source
    NDL  NII-ELS  IR 
Page Top