5 - The Even Cycle Problem
نویسنده
چکیده
For k ≥ 2 and l ≥ 0, let C (k, l) denote the family of all cycles of length l modulo k, and C (k) := C (l, 0). In proving the Even Cycle Theorem, we determine almost tight bounds on ex(n,C (k, l)) as well as a method for giving upper bounds on ex(n,C ) for various other infinite families of cycles. Bollobás [2] was the first to show that ex(n,C (k, l)) is linear in n for each pair (k, l) such that C (k, l) contains even cycles, by showing ex(n,C (k, l)) ≤ 1 k [(k + 1) − 1]n.
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