Minimal edge-coverings of pairs of sets
Journal of Combinatorial Theory Series B
Finding maximum square-free 2-matchings in bipartite graphs
Journal of Combinatorial Theory Series B
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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Given a simple bipartite graph G and an integer t ≥ 2, we derive a formula for the maximum number of edges in a subgraph H of G so that H contains no node of degree larger than t and H contains no complete bipartite graph Kt,t as a subgraph. In the special case t = 2 this fomula was proved earlier by Király (Square-free 2-matching in bipartite graphs, Technical Report of Egerváry Research Group, TR-2001013, November 1999 (www.cs.elte.hu/egres)), sharpening a result of Hartvigsen (in: G. Cornuejols, R. Burkard, G.J. Woeginger (Eds.), Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, Vol. 1610, Springer, Berlin, 1999, pp. 234-240). For any integer t ≥ 2, we also determine the maximum number of edges in a subgraph of G that contains no complete bipartite graph, as a subgraph, with more than t nodes. The proofs are based on a general min-max result of Frank and Jordán (J. Combin. Theory Ser. B 65(1) (1995) 73) concerning crossing bi-supermodular functions.