Stable Marriage with incomplete lists and ties - NP-hardness According to [1] finding a weakly stable matching in a stable marriage (or SM) instance with incomplete lists and ties is NP-Hard.

According to [2] a weakly stable matching in a hospital-residents (or HR) instance with ties always exists and one can be found by arbitrarily breaking the ties and applying one of the known algorithms for the HR problem.

Also HR with ties is a generalization of SM with incomplete lists and ties.

Isn't there a conflict here?

[1] K. Iwama, D. Manlove, S. Miyazaki and Y. Morita. Stable Marriage with Incomplete Lists and Ties. Automata, Languages and Programming, Lecture Notes in Computer Science, Springer Berlin / Heidelberg, 1999

[2] R. W. Irving, D. F. Manlove, and S. Scott. The Hospitals/Residents Problem with Ties. Algorithm Theory - SWAT 2000. Lecture Notes in Computer Science. Springer Berlin / Heidelberg

[3] V. Bansal , A. Agrawal , V. S. Malhotra. Polynomial time algorithm for an optimal stable assignment with multiple partners. Theoretical Computer Science 379 (2007) 317–328

[4] D.F. Manlove, R.W. Irving, K. Iwama, S. Miyazaki, and Y. Morita. Hard variants of stable marriage.Theoretical Computer Science 276(1-2):261-279.
The stable marriage instance with ties is solvable in polynomial time, whereas the stable marriage instance with incomplete lists and ties is NP-hard.

The same holds for the Hospitals/Residents problem.  So there is no conflict between [1] and [2].