An efficient O(|V(S)|^3) algorithm computes the largest 2-regular subgraph in complete S-partite graphs via integer linear programming.
Sparse linear ensemble systems and structural controllability
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Largest $2$-regular Subgraphs in complete $S$-partite Graphs
An efficient O(|V(S)|^3) algorithm computes the largest 2-regular subgraph in complete S-partite graphs via integer linear programming.