Track / Stage 5 / 316 of 400 #916 of 1964

Problem 916

AIME late

Combinatorics Difficulty 5.7 Prove it

(i) Prove: For all countable graphs with infinite vertex degrees, the unfriendly partition conjecture holds.
(ii) Can the proof in (i) be modified to also hold for countable graphs with finitely many vertices of finite degree?

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

Official solution

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