This research demonstrates that clean graphs of free groups aren't always special, suggesting new classifications.
We show that the fundamental group of a geometrically clean graph of finite rank free groups does not need to be virtually compact special, answering a question of Wise. This implies that the class of the virtually V H VH -clean graphs of finite rank free groups is a proper subclass of the class of virtually geometrically clean graphs of finite rank free groups.
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Kasia Jankiewicz (2026) studied this question.
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