Erdős's 1985 growth question for critical edge sets in k-vertex-critical graphs is answered affirmatively for every k > 4 via f_k(n) = Ω(n^(1/3)), and a first upper bound f_k(n) = O(n/(log n)^Ω(1)) is given for all k ≥ 4.
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Critical edge sets in vertex-critical graphs
Erdős's 1985 growth question for critical edge sets in k-vertex-critical graphs is answered affirmatively for every k > 4 via f_k(n) = Ω(n^(1/3)), and a first upper bound f_k(n) = O(n/(log n)^Ω(1)) is given for all k ≥ 4.