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A survey of graphs with known or bounded crossing numbers. (English) Zbl 1453.05024

Summary: We present, to the best of the authors’ knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories: specifically, results for general graph families, results for graphs arising from various graph products, and results for recursive graph constructions.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
05C75 Structural characterization of families of graphs
05C76 Graph operations (line graphs, products, etc.)

Software:

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Full Text: arXiv Link

Online Encyclopedia of Integer Sequences:

a(n) = (5/32)*4^n - floor((n^2 + 1)/2)*2^(n - 2).

References:

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