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Popular Matching in Roommates Setting Is NP-hard:

Gupta, Sushmita ; Misra, Pranabendu ; Saurabh, Saket.
ACM Transactions on Computation Theory (TOCT).  13 (2021)  2 - p. 1-20 , 2021
Link: https://dl.acm.org/doi/10.1145/3442354