Formal target: Corpus.Erdos572.erdos_572

Show that for $k\geq 3$ $$\mathrm{ex}(n;C_{2k})\gg n^{1+\frac{1}{k}}.$$ This problem is #46 in Extremal Graph Theory in the graphs problem collection.

Exact formal statement

∀ (k : Nat),
  LE.le.{0} 3 k →
    Exists.{1} fun c =>
      And (GT.gt.{0} c 0)
        (Filter.Eventually.{0}
          (fun n =>
            LE.le.{0}
              (HMul.hMul.{0, 0, 0} c
                (HPow.hPow.{0, 0, 0} (Nat.cast.{0} n) (HAdd.hAdd.{0, 0, 0} 1 (HDiv.hDiv.{0, 0, 0} 1 (Nat.cast.{0} k)))))
              (Nat.cast.{0} (SimpleGraph.extremalNumber.{0} n (SimpleGraph.cycleGraph (HMul.hMul.{0, 0, 0} 2 k)))))
          Filter.atTop.{0})

This target is a formal statement, not a proof of the problem.

Environment availability: available.

Public accepted solutions (paginated API)

Public JSON record