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  • Hamiltonian cycles in cubic Cayley graphs : the (2, 4k, 3) case
    Glover, Henry ; Kutnar, Klavdija, 1980- ; Marušič, Dragan
    It was proved by Glover and Marušič (J. Eur. Math. Soc. 9:775-787, 2007), that cubic Cayley graphs arising from groups ▫$G = \langle a, x \vert a^2 = x^s= (ax)^3 = 1, \dots \rangle$▫ having a ... ▫$(2,s,3)$▫-presentation, that is, from groups generated by an involution ▫$a$▫ and an element ▫$x$▫ of order ▫$s$▫ such that their product ▫$ax$▫ has order 3, have a Hamiltonian cycle when ▫$|G|$▫ (and thus also ▫$s$▫) is congruent to 2 modulo 4, and have a Hamiltonian path when ▫$|G|$▫ is congruent to 0 modulo 4. In this article the existence of a Hamiltonian cycle is proved when apart from ▫$|G|$▫ also ▫$s$▫ is congruent to 0 modulo 4, thus leaving ▫$|G|$▫ congruent to 0 modulo 4 with ▫$s$▫ either odd or congruent to 2 modulo 4 as the only remaining cases to be dealt with in order to establish existence of Hamiltonian cycles for this particular class of cubic Cayley graphs.
    Vir: Journal of algebraic combinatorics. - ISSN 0925-9899 (Vol. 30, no. 4, 2009, str. 447-475)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2009
    Jezik - angleški
    COBISS.SI-ID - 1024072020
    DOI

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