Dense Minors In Graphs Of Large Girth

We show that a graph of girth greater than 6 log k+3 and minimum degree at least 3 has a minor of minimum degree greater than k. This is best possible up to a factor of at most 9/4. As a corollary, every graph of girth at least 6 log r+3 log log r+c and minimum degree at least 3 has a K r minor.

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Correspondence to Reinhard Diestel.

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Diestel, R., Rempel, C. Dense Minors In Graphs Of Large Girth. Combinatorica 25, 111–116 (2004). https://doi.org/10.1007/s00493-005-0009-3

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Mathematics Subject Classification (2000):

  • 05C35
  • 05C83