Matching extendibility in hypercubes
نویسندگان
چکیده
In a bipartite graph G, a set S ⊆ V (G) is deficient if |N(S)| < |S|. A matching M (with vertex set U) is k-suitable if G − U has no deficient set of size less than k. Let fk(d) be the maximum r such that in the d-dimensional hypercube Qd every k-suitable matching having size at most r extends to a perfect matching. We generalize results of Limaye and Sarvate by proving that fk(d) = k(d− k) + ( k−1 2 ) for k ≤ d− 3. To this end we prove lower bounds on the sizes of neighborhoods of vertex sets in Qd. We also prove that every induced matching in Qd extends to a perfect matching.
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