Hamiltonicity of Cubic Cayley Graphs
| dc.creator | Glover, Henry | |
| dc.creator | Marusic, Dragan | |
| dc.date | 2005-08-31 | |
| dc.date.accessioned | 2026-07-07T05:22:51Z | |
| dc.date.available | 2026-07-07T05:22:51Z | |
| dc.description | Following 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.description | 13 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0508647 | |
| dc.identifier | http://arxiv.org/abs/math/0508647 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76222 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 05C25, 20B25 | |
| dc.title | Hamiltonicity of Cubic Cayley Graphs | |
| dc.type | text |