Cyclic cutwidths of the two-dimensional ordinary and cylindrical meshes Original Research Article

The cutwidth problem is to find a linear layout of a network so that the maximal number of cuts of a line separating consecutive vertices is minimized (see e.g. ). A related and more natural problem is the cyclic cutwidth when a circular layout is considered. The main question is to compare both measures cw and ccw for specific networks, whether adding an edge to a path and forming a cycle reduces the cutwidth essentially. We prove exact values for the cyclic cutwidths of the two-dimensional ordinary and cylindrical meshes Pm×Pn and Pm×Cn, respectively. Especially, if m⩾n+3, then ccw(Pm×Pn)=cw(Pm×Pn)=n+1 and if n is even then ccw(Pn×Pn)=n−1 while cw(Pn×Pn)=n+1 and if m⩾2,n⩾3, then ccw(Pm×Cn)=min{m+1,n+2}.