Hamilton paths in Cayley graphs on Coxeter groups: I

We consider several families of Cayley graphs on the finite Coxeter groups A_n, B_n, and D_n with regard to the problem of whether they are Hamilton-laceable or Hamilton-connected. It is known that every connected bipartite Cayley graph on A_n, n ≥ 2, whose connection set contains only transpositions and has valency at least three is Hamilton-laceable. We obtain analogous results for connected bipartite Cayley graphs on B_n, and for connected Cayley graphs on D_n. Non-bipartite examples arise for the latter family.