Graph minors and linkages

Bollobás and Thomason showed that every 22k-connected graph is k-linked. Their result used a dense graph minor. In this paper we investigate the ties between small graph minors and linkages. In particular, we show that a 6-connected graph with a K− 9 minor is 3-linked. Further, we show that a 7-connected graph with a K− 9 minor is (2, 5)-linked. Finally, we show that a graph of order n and size at least 7n − 29 contains a K−− 9 minor.

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