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Oct 2, 2017 at 8:53 history edited Ilya Bogdanov CC BY-SA 3.0
added 107 characters in body
Oct 1, 2017 at 17:49 comment added Lviv Scottish Book The author of the problem informed me that an additional condition (that $H$ is a tree) should be added. So, your counterexample does not work for this more special case.
Sep 30, 2017 at 11:30 history answered Ilya Bogdanov CC BY-SA 3.0