Hamilton paths in Cayley graphs on Coxeter groups: I

Abstract

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.