Hamiltonicity of Cubic Cayley Graphs

dc.creatorGlover, Henry
dc.creatorMarusic, Dragan
dc.date2005-08-31
dc.date.accessioned2026-07-07T05:22:51Z
dc.date.available2026-07-07T05:22:51Z
dc.descriptionFollowing a problem posed by Lovász in 1969, it is believed that every connected vertex-transitive graph has a Hamilton path. This is shown here to be true for cubic Cayley graphs arising from groups having a $(2,s,3)$-presentation, that is, for groups $G=\la a,b| a^2=1, b^s=1, (ab)^3=1, etc. \ra$ generated by an involution $a$ and an element $b$ of order $s\geq3$ such that their product $ab$ has order 3. More precisely, it is shown that the Cayley graph $X=Cay(G,\{a,b,b^{-1}\})$ has a Hamilton cycle when $|G|$ (and thus $s$) is congruent to 2 modulo 4, and has a long cycle missing only two vertices (and thus necessarily a Hamilton path) when $|G|$ is congruent to 0 modulo 4.
dc.description13 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/math/0508647
dc.identifierhttp://arxiv.org/abs/math/0508647
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76222
dc.subjectCombinatorics
dc.subjectGroup Theory
dc.subject05C25, 20B25
dc.titleHamiltonicity of Cubic Cayley Graphs
dc.typetext

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