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Topics in Topological Graph Theory by Jonathan L. Gross, Robin J. Wilson, Lowell W. Beineke

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7Crossing numbers

R. BRUCE RICHTER and G. SALAZAR

1. Introduction

2. What is the crossing number?

3. General bounds

4. Applications to geometry

5. Crossing-critical graphs

6. Other families of graphs

7. Algorithmic questions

8. Drawings in other surfaces

9. Conclusion

References

        The crossing number of a graph G is the smallest number of pairwise crossings of edges among all drawings of G in the plane. In the last decade, there has been significant progress on a true theory of crossing numbers. There are now many theorems on the crossing number of a general graph and the structure of crossing-critical graphs, whereas in the past, most results were about the crossing numbers of either individual graphs or the members of special families ...

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