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Extremal Problems for the Family of $k$-Strongly Connected Digraphs

math.CO · 2026-05-02 · unverdicted · novelty 6.0

The saturation number sat(n, D_k) is exactly (k-1)(2n-k) + binom(n-k+1,2); the extremal number is at most binom(n-k+1,2) + (17/6)(k-1)(n-k+1) for n >= 3(k-1), with a conjecture that it equals binom(n,2) + (3/2)(k-4/3)(n-k+1) for large n.

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  • Extremal Problems for the Family of $k$-Strongly Connected Digraphs math.CO · 2026-05-02 · unverdicted · none · ref 1

    The saturation number sat(n, D_k) is exactly (k-1)(2n-k) + binom(n-k+1,2); the extremal number is at most binom(n-k+1,2) + (17/6)(k-1)(n-k+1) for n >= 3(k-1), with a conjecture that it equals binom(n,2) + (3/2)(k-4/3)(n-k+1) for large n.