TL;DR
This paper disproves a conjecture by Imrich and Müller concerning the rank of the intersection of subgroups within free groups, challenging previous assumptions in the field.
Contribution
The paper provides a counterexample that refutes the conjecture, advancing understanding of subgroup intersections in free groups.
Findings
The conjecture by Imrich and Müller is false.
Counterexamples demonstrate the limits of previous bounds.
The result impacts the study of subgroup intersections.
Abstract
A conjecture of Imrich and M\"uller on rank of the intersection of subgroups of free groups is disproved.
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