## Graph Planarization and Skewness

by
Robert Cimikowski

Citations: | 8 - 0 self |

### BibTeX

@MISC{Cimikowski_graphplanarization,

author = {Robert Cimikowski},

title = {Graph Planarization and Skewness},

year = {}

}

### OpenURL

### Abstract

The problem of finding a maximum spanning planar subgraph of a nonplanar graph is NP-Complete. Several heuristics for the problem have been devised but their worst-case performance is unknown, although a trivial lower bound of 1/3 the optimum number of edges is easily shown. We discuss a new heuristic, based on spanning trees, for generating a subgraph with size at least 2/3 of the optimum for any input graph. The skewness of the n-dimensional hypercube Qn is also derived. Finally, we explore the relationship between the skewness and crossing number of a graph.