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The extremal function for cycles of length ℓ mod k
[article]
2016
arXiv
pre-print
Burr and Erdős conjectured that for each k,ℓ∈ Z^+ such that k Z + ℓ contains even integers, there exists c_k(ℓ) such that any graph of average degree at least c_k(ℓ) contains a cycle of length ℓ mod k. This conjecture was proved by Bollobás, and many successive improvements of upper bounds on c_k(ℓ) appear in the literature. In this short note, for 1 ≤ℓ≤ k, we show that c_k(ℓ) is proportional to the largest average degree of a C_ℓ-free graph on k vertices, which determines c_k(ℓ) up to an
arXiv:1606.08532v1
fatcat:26ryzcr6afhqznf6fj2czj6mby