On the crossing numbers of Cartesian products with paths

Authors:
Drago Bokal
Affiliations:
Department of Mathematics, Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia
Venue:
Journal of Combinatorial Theory Series B
Year:
2007

Citing 2
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The crossing number of Cm × Cn is as conjectured for n ≥ m(m + 1)

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On the crossing numbers of Km⊔Cn and Km,l⊔Pn

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Crossing number additivity over edge cuts

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Abstract

Using a newly introduced operation on graphs and its counterpart on graph drawings, we prove the conjecture of Jendrol' and Scerbova from 1982 about the crossing number of the Cartesian product K"1","m@?P"n. Our approach is applicable to the capped Cartesian products of P"n with any graph containing a dominating vertex.