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From the Wikipedia entry on Tutte 12-cage , it is stated that the crossing number of Tutte 12-cage is 170, but the cited references do not seem to provide sufficient explanation for this.

enter image description here

  • Exoo, G. "Rectilinear Drawings of Famous Graphs".
  • Pegg, E. T. and Exoo, G. "Crossing Number Graphs." Mathematica J. 11, 2009.

At least, Exoo, G. only mentioned that the graph has a straight-line crossing drawing with 170 crossings, but they did not claim that its crossing number is 170.

enter image description here

I would like to know which specific literature explicitly states that the crossing number of this graph is 170. Otherwise, this entry is very imprecise.

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    $\begingroup$ I'd guess that this is just another case where Wikipedia misinterprets its sources. You could try verifying the number yourself using the Crossing Number Web Compute, though the Tutte 12-cage may be a bit too big. $\endgroup$
    – Timothy Chow
    Commented Feb 21, 2023 at 15:53
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    $\begingroup$ Thanks. 170 may be wrong as I see that an embedding with rectilinear crossing number 166 was found by G. Exoo (pers. comm., May 12, 2019) which QuickCross was able to reduce to a graph crossing number of 165 (E. Weisstein, May 12, 2019). in this link mathworld.wolfram.com/Tutte12-Cage.html $\endgroup$
    – Licheng Zhang
    Commented Feb 21, 2023 at 15:59
  • $\begingroup$ Crossing Number Web Compute seems to only support graphs with up to 100 vertices. $\endgroup$
    – Licheng Zhang
    Commented Feb 22, 2023 at 4:35
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    $\begingroup$ I've updated Wikipedia. $\endgroup$
    – domotorp
    Commented Feb 27, 2023 at 12:27

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