A survey of graphs with known or bounded crossing numbers

Abstract

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.

arXiv comment95 pages. Dynamic survey, last updated December 2021

References in corpus (6)

• Improved bounds for the crossing numbers of K_m,n and K_n
• Crossing numbers of complete tripartite and balanced complete multipartite graphs
• Coloring graphs with crossings
• On the crossing number of some complete multipartite graphs
• The crossing number of folded hypercubes
• Disproof of a conjecture by Erdős and Guy on the crossing number of hypercubes