A Weighted kt, t-Free t-Factor Algorithm for Bipartite Graphs
Mathematics of Operations Research
A weighted Kt, t-free t-factor algorithm for bipartite graphs
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
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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Frank examined the maximum $K_{t,t}$-free $t$-matching problem of simple bipartite graphs. As the $C_6$-free $2$-matching problem is NP-hard (Geelen), this is a promising generalization of restricted $2$-matchings. Given an arbitrary family $\mathcal{T}$ of $K_{t,t}$-subgraphs of the underlying graph, a $\mathcal{T}$-free $t$-matching is a subgraph of maximum degree at most $t$ that contains no member of $\mathcal{T}$. We show that the maximum size $\mathcal{T}$-free $t$-matching problem also admits a nice min-max formula. Given an integer cost function on the edge-set which is vertex-induced on any member of $\mathcal{T}$, we also show an integer min-max formula for the maximum cost of $\mathcal{T}$-free $t$-matchings. As the maximum cost $C_4$-free 2-matching problem is NP-hard (Kira´ly), we cannot expect a nice characterization in general.