Hamilton paths in Cayley graphs on Coxeter groups: I

Abstract

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