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On the spectrum of the forced matching number of graphs. (English) Zbl 1056.05110

Let \(G\) be a graph that admits a perfect matching. A forcing set for a perfect matching \(M\) of \(G\) is a subset \(S\) of \(M\), such that \(S\) is contained in no other perfect matching of \(G\). The smallest cardinality of a forcing set of \(M\) is called the forced matching number. The authors study the spectrum of possible forced matching numbers for the grids \(P_m\times P_n\), and they investigate forcing sets for the product of a cycle and a path and the product of two cycles.

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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