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In byzantine generals problem, it is proved that one third or more generals should be loyal, or the problem is unsolvable from a mathematical standpoint.

Does Bitcoin network follow the same rule? How does it ensure the minimum number of honest nodes?

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The result from the BFT literature that tells us that it is impossible to achieve consensus with more than 1/3 or parties being malicious depends on a few assumptions which are different from the security assumptions that Bitcoin makes.

In particular, BFT algorithms usually are designed to give guaranteed finality, where as in Bitcoin this is only probabilistic (there is always a small chance an attacker could get lucky and mine many blocks in a row, but for longer and longer forks, this chance is vanishingly small).

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