Timeline for Hamiltonian cycles and fundamental groups
Current License: CC BY-SA 3.0
7 events
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| Aug 7, 2014 at 23:11 | history | edited | David White | CC BY-SA 3.0 |
Fixed typo
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| Sep 16, 2011 at 5:05 | comment | added | Robert Bell | The papers by Glover and Marusic use an embedding of the Cayley graph into a surface to construct Hamilton cycles. They show that if a finite group $Q$ of order congruent to 2 modulo 4 is a quotient of $G = (a, b ; a^2, b^s, (ab)^3)$, where $s \geq 3$, then the Cayley graph of $Q$ with respect to the generating set $\{a, b, b^{-1}\}$ has a Hamilton cycle. See arxiv.org/PS_cache/math/pdf/0508/0508647v1.pdf for instance. | |
| Aug 4, 2011 at 23:55 | comment | added | Joseph O'Rourke | Here is more info on the paper Geoff cited. Breuer, T.; Guralnick, R. M.; Lucchini, A.; Maróti, A.; Nagy, G. P. Hamiltonian cycles in the generating graphs of finite groups. Bull. Lond. Math. Soc. 42 (2010), no. 4, 621–633: "For a finite group $G$ let $\Gamma(G)$ denote the graph defined on the non-identity elements of $G$ in such a way that two distinct vertices are connected by an edge if and only if they generate $G$. In this paper it is shown that the graph $\Gamma(G)$ contains a Hamiltonian cycle for many finite groups $G$." | |
| Aug 4, 2011 at 23:50 | history | edited | Gjergji Zaimi | CC BY-SA 3.0 |
added 1 characters in body
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| Aug 4, 2011 at 23:23 | comment | added | Geoff Robinson | MR2669683 may be relevant | |
| Aug 4, 2011 at 23:21 | comment | added | Gerhard Paseman | I think the heuristic should be "when a vertex-regular graph has a Hamiltonian cycle, it has exponentially many", or some similar condition that does not require a large automorphism group. Gerhard "Ask Me About System Design" Paseman, 2011.08.04 | |
| Aug 4, 2011 at 23:14 | history | asked | Gjergji Zaimi | CC BY-SA 3.0 |