You don't necessarily have any DNA from any particular ancestor, but they would be your ancestor. This is explained in the article I linked. That means that if everybody's ancestors converged in 5500 BC, and at least one person had a Neanderthal as their ancestor, everyone has a Neanderthal ancestor.
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Common ancestors are in all humans IIRC. While say Neanderthal DNA is only in subset of populations.
You don't necessarily have any DNA from any particular ancestor, but they would be your ancestor. This is explained in the article I linked. That means that if everybody's ancestors converged in 5500 BC, and at least one person had a Neanderthal as their ancestor, everyone has a Neanderthal ancestor.