A tour problem on a toroidal board

In this paper we study a tour problem that we came cross while studying biembeddings and Heffter arrays, see [D.S. Archdeacon, Heffter arrays and biembedding graphs on surfaces, Electron. J. Combin. 22 (2015) #P1.74]. Let A be an n\times m toroidal array consisting of filled cells and empty cells. Assume... Show more