Bounding the crossing number of a graph in terms of the crossing number of a minor with small maximum degree

Authors:
Enrique Garcia-Moreno;Gelasio Salazar
Affiliations:
Empresa 109, Col. Mixcoac Mexico DF, 02920 Mexico;IICO-UASLP, Av. Karakorum 1470, Lomas 4ta. Seccion, San Luis Potosi SLP, 78210 Mexico
Venue:
Journal of Graph Theory
Year:
2001

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Abstract

We show that if G has a minor M with maximum degree at most 4, then the crossing number of G in a surface Σ is at least one fourth the crossing number of M in Σ. We use this result to show that every graph embedded on the torus with representativity r ≥ 6 has Klein bottle crossing number at least ⌊2r-3⌋2-64. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 168–173, 2001