On subgraphs of random Cayley sum graphs

Random induced subgraphs of Cayley graphs induced by transpositions

In this paper we study random induced subgraphs of Cayley graphs of the symmetric group induced by an arbitrary minimal generating set of transpositions. A random induced subgraph of this Cayley graph is obtained by selecting permutations with independent probability, λn. Our main result is that for any minimal generating set of transpositions, for probabilities λn = 1+ǫn n−1 where n− 1 3 +δ ≤ ...

Random Subgraphs of Cayley Graphs over p-Groups

On the girth of random Cayley graphs

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 quest...

On K4-Free Subgraphs of Random Graphs

On small subgraphs of random graphs