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We give a complete description of the congruences on the partition monoid$P_X$ and the partial Brauer monoid $PB_X$, where $X$ is an arbitrary infiniteset, and also of the lattices formed by all such congruences. Our resultscomplement those from a recent article of East, Mitchell, Ruskuc and Torpey,which deals with the finite case. As a consequence of our classificationresult, we show that the congruence lattices of $P_X$ and $PB_X$ are isomorphicto each other, and are distributive and well quasi-ordered. We also calculatethe smallest number of pairs of partitions required to generate any congruence;when this number is infinite, it depends on the cofinality of certain limitcardinals.

Congruences on infinite partition and partial Brauer monoids