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Some recent results in topological graph theory

  • Part II: Contributed Papers Expository Review Articles
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Graphs and Combinatorics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 406))

Abstract

This paper examines a number of recent results in topological graph theory. Invariants such as genus, thickness, skewness, crossing number, and local crossing number are introduced and related to one another. We then deal with topological techniques in the theory of chromatic numbers, and state a very ambitious meta-conjecture which is quite useful in generating true theorems. In closing, we attempt to suggest appropriate directions for further research in topological graph theory, and we give a few results to indicate the richness of the terrain.

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  1. Case Western Reserve University, USA

    Paul C. Kainen

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  1. Paul C. Kainen
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Ruth A. Bari Frank Harary

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© 1974 Springer-Verlag Berlin

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Kainen, P.C. (1974). Some recent results in topological graph theory. In: Bari, R.A., Harary, F. (eds) Graphs and Combinatorics. Lecture Notes in Mathematics, vol 406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066436

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  • DOI: https://doi.org/10.1007/BFb0066436

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