# Finding large planar subgraphs and large subgraphs of a given genus

Session 5

First Online:

## Abstract

We consider the MAXIMUM PLANAR SUBGRAPH problem — given a graph *G*, find a largest planar subgraph of *G*. This problem has applications in circuit layout, facility layout, and graph drawing. We improve to 4/9 the best known approximation ratio for the MAXIMUM PLANAR SUBGRAPH problem. We also consider a generalization of the previous problem, the MAXIMUM GENUS *D* SUBGRAPH problem — given a connected graph *G*, find a maximum subgraph of *G* of genus at most *D*. For the latter problem, we present a simple algorithm whose approximation ratio is 1/4.

## Preview

Unable to display preview. Download preview PDF.

## References

- [CFFK96]G. Călinescu, C. G. Fernandes, U. Finkler and H. Karloff, “A Better Approximation Algorithm for Finding Planar Subgraphs”,
*Proc.*7th*Annual ACM-SIAM Symp. on Discrete Algorithms*, 1996.Google Scholar - [CN85]N. Chiba and T. Nishizeki, “Arboricity and Subgraph Listing Algorithms”,
*SIAM Journal of Computing*, 14:210–223, 1985.Google Scholar - [F92]L. R. Foulds,
*Graph Theory Applications*, Springer-Verlag, New York, 1992.Google Scholar - [GS85]H. N. Gabow and M. Stallmann, “Efficient Algorithms for Graphic Matroid Intersection and Parity”,
*Automata, Language and Programming:*12^{th}*Collog., Lecture Notes in Computer Science*, Vol. 194, 210–220, 1985.Google Scholar - [LG77]P. C. Liu and R. C. Geldmacher, “On the Deletion of Nonplanar Edges of a Graph”,
*Proc.*10th*Southeastern Conference on Combinatorics, Graph Theory, and Computing*, 727–738, 1977.Google Scholar - [LP86]L. Lovász and M. D. Plummer,
*Matching Theory*, Elsevier Science, Amsterdam, 1986.Google Scholar - [TDB88]R. Tamassia, G. Di Battista and C. Batini, “Automatic Graph Drawing and Readability of Diagrams”,
*IEEE Transactions on Systems, Man and Cybernetics*, 18:61–79, 1988.Google Scholar - [Th89]C. Thomassen, “The Graph Genus Problem is NP-Complete”,
*Journal of Algorithms*, 10:568–576, 1989.Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1996