Hamilton cycles in directed Euler tour graphs (Q1095154)

The directed Euler tour graph of a directed Eulerian multigraph without loops D, denoted by Eu(D), is an undirected simple graph defined as follows: The vertices of Eu(D) are directed Euler tours of D, and two directed Euler tours E and F are adjacent in Eu(D) if they can be obtained from each other by a T-transformation which is defined in the paper. The authors prove that if D is a directed Euler graph having at least three directed Euler tours then any edge of Eu(D) is contained in a Hamilton cycle of Eu(D).