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Perfect matchings in a class of bipartite graphs. (English) Zbl 0738.05064

Denote \(\{1,\dots,n\}\) the vertex set of the graph \(G\). Let \(I_ p=\{i_ 1,i_ 2,\dots i_{2p}\}\subset\{1,\dots,n\}\) and \(i_ j<i_{j+1}\). Denote \(G(n,I_ p)\) the graph having the edges \((1,2),(2,3),\dots,((n-1),n),(n,1)\) and \((i_ j,i_{2p-j+1})\), \(j=1,\dots,p\). The paper establishes some relations for the number of perfect matchings of \(G(n,I_ p)\).

MSC:

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