## The Thickness of Graphs: A Survey (1998)

Venue: | Graphs Combin |

Citations: | 18 - 0 self |

### BibTeX

@ARTICLE{Mutzel98thethickness,

author = {Petra Mutzel and Thomas Odenthal and Mark Scharbrodt},

title = {The Thickness of Graphs: A Survey},

journal = {Graphs Combin},

year = {1998},

volume = {14},

pages = {59--73}

}

### Years of Citing Articles

### OpenURL

### Abstract

We give a state-of-the-art survey of the thickness of a graph from both a theoretical and a practical point of view. After summarizing the relevant results concerning this topological invariant of a graph, we deal with practical computation of the thickness. We present some modifications of a basic heuristic and investigate their usefulness for evaluating the thickness and determining a decomposition of a graph in planar subgraphs. Key words: Thickness, maximum planar subgraph, branch and cut 1 Introduction In VLSI circuit design, a chip is represented as a hypergraph consisting of nodes corresponding to macrocells and of hyperedges corresponding to the nets connecting the cells. A chip-designer has to place the macrocells on a printed circuit board (which usually consists of superimposed layers), according to several designing rules. One of these requirements is to avoid crossings, since crossings lead to undesirable signals. It is therefore desirable to find ways to handle wi...