OpenAI reports the second Kahn–Kalai threshold bound
- Mathematics
For every finite simple graph H with h≥1 edges and at most n vertices, the threshold for G(n,p) to contain an ordinary copy of H is at most C p_E(n,H)(1+log₂ h) for a universal C.
OpenAI reports the second Kahn–Kalai threshold bound
- Mathematics
For every finite simple graph H with h≥1 edges and at most n vertices, the threshold for G(n,p) to contain an ordinary copy of H is at most C p_E(n,H)(1+log₂ h) for a universal C.
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Read the background
For every finite simple graph H with h≥1 edges and at most n vertices, the threshold for G(n,p) to contain an ordinary copy of H is at most C p_E(n,H)(1+log₂ h) for a universal C.
Why it matters
If correct, resolves the second Kahn–Kalai conjecture with a logarithm depending on target edge count.
What counts as progress
Is a graph’s random-containment threshold within a logarithmic factor of its expectation threshold?
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