The cyclic cutwidth of trees

Embedding of C_n^2 and C_(n-1)^2+K_1 in to Arbitrary Tree

“…Most of the work on the dilation-sum problem and the dilation problem are for the particular case in which the host graph is a path, or a cycle [20].The concept of cutwidth is a special case of congestion when the host graph is a path [11,26,29]. There are several results on the congestion problem for various architectures such as trees into cycles [11], trees into stars [28], trees into hypercubes [4,22], hypercubes into grids [5,6,25], complete binary trees into grids [23], and ladders and caterpillars into hypercubes [7,10]. There are also other general results on embeddings [2].…”

Embedding of cycles and wheels into arbitrary trees

“…The concept of cutwidth is a special case of congestion when the host graph is a path [11,26,29]. There are several results on the congestion problem for various architectures such as trees into cycles [11], trees into stars [28], trees into hypercubes [4,22], hypercubes into grids [5,6,25], complete binary trees into grids [23], and ladders and caterpillars into hypercubes [7,10].…”

Cyclic cutwidths of the two-dimensional ordinary and cylindrical meshes

“…One of the main questions is to compare both measures, denoted by cw(G) and ccw(G), respectively, for a speciÿc network G, whether adding an edge to a path and forming a cycle reduces the cutwidth essentially. In [6,12], it is shown that the cyclic cutwidth equals the cutwidth in case of trees. For the toroidal mesh, the cyclic cutwidth is roughly half of the cutwidth [15].…”