ULethbridge Number Theory and Combinatorics Seminar: Iren Darijani

A directed graph H consists of a set V(H) of vertices together with a subset A(H) of V(H)×V(H) which are called arcs. A hamiltonian dipath in a digraph is a dipath that visits each vertex exactly once. The Cartesian product H₁◻H₂ of two digraphs H₁ and H₂ is the digraph with vertex set V(H₁)×V(H₂) where the vertex (u₁,v₁) is joined to (u₂,v₂) by an arc if and only if either u₁=u₂ and v₁v₂∈A(H₂) or v₁=v₂ and u₁u₂∈A(H₁). The Cartesian product C_m◻C_n, where C_m and C_n are two dicycles, is called the toroidal digrid with m rows and n columns. In this talk, we see that there exist two arc-disjoint hamiltonian dipaths in every toroidal digrid.