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
An algorithm for (n-3)-connectivity augmentation problem: Jump system approach
Journal of Combinatorial Theory Series B
Restricted b-matchings in degree-bounded graphs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
A proof of Cunningham's conjecture on restricted subgraphs and jump systems
Journal of Combinatorial Theory Series B
A simple algorithm for finding a maximum triangle-free 2-matching in subcubic graphs
Discrete Optimization
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For a simple bipartite graph and an integer t ≥ 2, we consider the problem of finding a minimum-weight kt, t-free t-factor, which is a t-factor containing no complete bipartite graph kt, t as a subgraph. When t = 2, this problem amounts to the square-free 2-factor problem in a bipartite graph. For the unweighted square-free 2-factor problem, a combinatorial algorithm is given by Hartvigsen, and the weighted version of the problem is NP-hard. For general t, Pap designed a combinatorial algorithm for the unweighted version, and Makai gave a dual integral description of kt, t-free t-matchings for a certain case where the weight vector is vertex-induced on any subgraph isomorphic to kt, t. For this class of weight vectors, we propose a strongly polynomial algorithm to find a minimum-weight kt, t-free t-factor. 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 one.