Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
SIAM Journal on Discrete Mathematics
Minimal edge-coverings of pairs of sets
Journal of Combinatorial Theory Series B
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Restricted t-matchings in bipartite graphs
Discrete Applied Mathematics - Submodularity
Primal-dual approach for directed vertex connectivity augmentation and generalizations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Finding maximum square-free 2-matchings in bipartite graphs
Journal of Combinatorial Theory Series B
Combinatorial algorithms for matchings, even factors and square-free 2-factors
Mathematical Programming: Series A and B
On Maximum Cost $K_{t,t}$-Free $t$-Matchings of Bipartite Graphs
SIAM Journal on Discrete Mathematics
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For a simple bipartite graph and an integer t ≥ 2, we consider the problem of finding a minimum-weight t-factor under the restriction that it contains no complete bipartite graph Kt, t as a subgraph. When t = 2, this problem amounts to the minimum-weight square-free 2-factor problem in a bipartite graph, which is NP-hard. We propose, however, a strongly polynomial algorithm for a certain case where the weight vector is vertex-induced on any subgraph isomorphic to Kt, t. The algorithm adapts the unweighted algorithms of Hartvigsen and Pap, and a primal-dual approach to the minimum-cost flow problem. The algorithm is fully combinatorial, and thus provides a dual integrality theorem, which is tantamount to Makai's theorem dealing with maximum-weight Kt, t-free t-matchings.