abstract
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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 numberat least [2r/3]2/64. © 2001 John Wiley %26amp; Sons, Inc.
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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 numberat least [2r/3]2/64. © 2001 John Wiley & Sons, Inc.
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