Track / Stage 5 / 318 of 400 #918 of 1964

Problem 918

AIME late

Combinatorics Difficulty 5.8 Prove it

22. Let $\mathcal{B}$ be a maximum-sized clique in graph $G$ . Prove: Each tree decomposition of $G$ with minimum width has a unique part covering $\mathcal{B}$ .

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

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.