On the girth of random Cayley graphs
نویسندگان
چکیده
We prove that random d-regular Cayley graphs of the symmetric group asymptotically almost surely have girth at least (logd−1 |G|) /2 and that random d-regular Cayley graphs of simple algebraic groups over Fq asymptotically almost surely have girth at least logd−1 |G|/ dim(G). For the symmetric p-groups the girth is between log log |G| and (log |G|) with α < 1. Several conjectures and open questions are presented.
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ورودعنوان ژورنال:
- Random Struct. Algorithms
دوره 35 شماره
صفحات -
تاریخ انتشار 2009