6 research outputs found

    Many, many more intrinsically knotted graphs

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    We list more than 200 new examples of minor minimal intrinsically knotted graphs and describe many more that are intrinsically knotted and likely minor minimal.Comment: 19 pages, 16 figures, Appendi

    Complete Minors in Complements of Non-Separating Planar Graphs

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    We prove that the complement of any non-separating planar graph of order 2nโˆ’32n-3 contains a KnK_n minor, and argue that the order 2nโˆ’32n-3 is lowest possible with this property. To illustrate the necessity of the non-separating hypothesis, we give an example of a planar graph of order 11 whose complement does not contain a K7K_7 minor. We argue that the complements of planar graphs of order 11 are intrinsically knotted. We compute the Hadwiger numbers of complements of wheel graphs.Comment: 13 pages, 8 figure
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