Abstract:
Improved lower bounds (compared with the known bounds of A. F. Sidorenko) are obtained for the number of mappings of a tree $D$ into a graph $\Gamma$ under the assumption that the degrees of the vertices of the tree take two values. These bounds are sharp also in a more general setting, when $\Gamma$ can be a weighted graph. The bounds also appear to be true for all trees $D$ with a specified number of edges.
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