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The Merrifield-Simmons conjecture holds for bipartite graphs
Let be a graph and the number of independent
(vertex) sets in . Then the Merrifield-Simmons conjecture states that the
sign of the term only depends on the parity of the distance of the vertices
in . We prove that the conjecture holds for bipartite graphs by
considering a generalization of the term, where vertex subsets instead of
vertices are deleted.Comment: 8 page