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Extending partial systems of distinct representatives. (English) Zbl 0738.05065
Summary: We determine a necessary and sufficient condition for a special class of families of sets to have the property that each partial SDR of cardinality \(d\) can be extended to a total SDR. This result is a generalization of a theorem of Brualdi and Csima concerning matching extension in regular bipartite graphs.

MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05A05 Permutations, words, matrices
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References:
[1] Brualdi, R.A.; Csima, J., Extending supermutation matrices in regular classes of matrices, Discrete math., 62, 99-101, (1986) · Zbl 0595.05014
[2] Plummer, M.D., On n-extendable graphs, Discrete math., 31, 201-210, (1980) · Zbl 0442.05060
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