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There are some C or Java programs available for computing crossing number, but not in wolfram language. But we can call it. One of them is QuickCross.

Import["!D://QuickCross//QC -g I~qkzXZLw", "Table"]
                      (*{{"CR", ":", 12}}*)

This is a bit like mathematica calling nauty-geng's results.

If one wishes to actually solve instances, Markus Chimani and Tilo Wiedera produced a mixed-integer linear program in 2016 that is able to compute crossing numbers for small graphs, complete with a proof file, and produced an online interface, Crossing Number Web Compute , where researchers can submit their owninstances.

The crossing number results of specific graphs can be referred to in the following review.

• Clancy K, Haythorpe M, Newcombe A. A survey of graphs with known or bounded crossing numbers[J]. arXiv preprint arXiv:1901.05155, 2019.

There are some C or Java programs available for computing crossing number, but not in wolfram language. But we can call it. One of them is QuickCross.

Import["!D://QuickCross//QC -g I~qkzXZLw", "Table"]
                      (*{{"CR", ":", 12}}*)

This is a bit like Mathematica calling nauty-geng's results.

If one wishes to actually solve instances, Markus Chimani and Tilo Wiedera produced a mixed-integer linear program in 2016 that is able to compute crossing numbers for small graphs, complete with a proof file, and produced an online interface, Crossing Number Web Compute , where researchers can submit their owninstances.

The crossing number results of specific graphs can be referred to in the following review.

• Clancy K, Haythorpe M, Newcombe A. A survey of graphs with known or bounded crossing numbers[J]. arXiv preprint arXiv:1901.05155, 2019.

There are some c or java programs available for computing crossing number, but not in wolfram language. But we can call it. One of them is QuickCross.

Import["!D://QuickCross//QC -g I~qkzXZLw", "Table"]
                      (*{{"CR", ":", 12}}*)

This is a bit like mathematica calling nauty-geng results.

If one wishes to actually solve instances, Markus Chimani and Tilo Wiedera produced a mixed-integer linear program in 2016 that is able to compute crossing numbers for small graphs, complete with a proof file, and produced an online interface, Crossing Number Web Compute , where researchers can submit their owninstances.

The crossing number results of specific graphs can be referred to in the following review.

• Clancy K, Haythorpe M, Newcombe A. A survey of graphs with known or bounded crossing numbers[J]. arXiv preprint arXiv:1901.05155, 2019.

There are some C or Java programs available for computing crossing number, but not in wolfram language. But we can call it. One of them is QuickCross.

Import["!D://QuickCross//QC -g I~qkzXZLw", "Table"]
                      (*{{"CR", ":", 12}}*)

This is a bit like mathematica calling nauty-geng's results.

If one wishes to actually solve instances, Markus Chimani and Tilo Wiedera produced a mixed-integer linear program in 2016 that is able to compute crossing numbers for small graphs, complete with a proof file, and produced an online interface, Crossing Number Web Compute , where researchers can submit their owninstances.

The crossing number results of specific graphs can be referred to in the following review.

• Clancy K, Haythorpe M, Newcombe A. A survey of graphs with known or bounded crossing numbers[J]. arXiv preprint arXiv:1901.05155, 2019.

There are some c or java programs available for computing crossing number, but not in mathematica languages. But we can call it. One of them is QuickCross.

Import["!D://QuickCross//QC -g I~qkzXZLw", "Table"]
                      (*{{"CR", ":", 12}}*)

This is a bit like mathematica calling nauty-geng results.

If one wishes to actually solve instances, Markus Chimani and Tilo Wiedera produced a mixed-integer linear program in 2016 that is able to compute crossing numbers for small graphs, complete with a proof file, and produced an online interface, Crossing Number Web Compute , where researchers can submit their owninstances.

The crossing number results of specific graphs can be referred to in the following review.

• Clancy K, Haythorpe M, Newcombe A. A survey of graphs with known or bounded crossing numbers[J]. arXiv preprint arXiv:1901.05155, 2019.

There are some c or java programs available for computing crossing number, but not in wolfram language. But we can call it. One of them is QuickCross.

Import["!D://QuickCross//QC -g I~qkzXZLw", "Table"]
                      (*{{"CR", ":", 12}}*)

This is a bit like mathematica calling nauty-geng results.

If one wishes to actually solve instances, Markus Chimani and Tilo Wiedera produced a mixed-integer linear program in 2016 that is able to compute crossing numbers for small graphs, complete with a proof file, and produced an online interface, Crossing Number Web Compute , where researchers can submit their owninstances.

The crossing number results of specific graphs can be referred to in the following review.

• Clancy K, Haythorpe M, Newcombe A. A survey of graphs with known or bounded crossing numbers[J]. arXiv preprint arXiv:1901.05155, 2019.