The congestion of n-cube layout on a rectangular grid

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

“…where the minimum is taken over all embeddings f of G into H. The congestion-sum problem [5,6] of a graph G into H is that of finding an embedding of G into H that induces the congestion-sum C (G, H). We are also interested in the minimum congestion of an edge, which is defined as…”

“…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].…”

Cutwidth of triangular grids

“…An exact formula for cutwidth on trees called "iterated caterpillars" appears in [12]. The cutwidth of n-dimensional hypercubes was studied in [2,11].…”