Abstract
Alon and Krivelevich proved that for every n-vertex subcubic graph H and every integer q≥2 there exists a (smallest) integer f=f(H,q) such that every Kf-minor contains a subdivision of H in which the length of every subdivision-path is divisible by q. Improving their superexponential bound, we show that f(H,q)≤212qn+8n+14q, which is optimal up to a constant multiplicative factor.
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