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.
Received: 22.05.2023
English version: Transactions of the Moscow Mathematical Society, 2023, Volume 84, Pages 97–144 DOI: https://doi.org/10.1090/mosc/353
Citation:
A. M. Leontovich, “A sharp lower bound for the number of mappings of a linear graph into an arbitrary graph and an inequality of A. F. Sidorenko”, Tr. Mosk. Mat. Obs., 84, no. 1, MCCME, M., 2023, 117–177; Trans. Moscow Math. Soc., 84 (2023), 97–144
\Bibitem{Leo23}
\by A.~M.~Leontovich
\paper A sharp lower bound for the number of mappings of a linear graph into an arbitrary graph and an inequality of A. F. Sidorenko
\serial Tr. Mosk. Mat. Obs.
\yr 2023
\vol 84
\issue 1
\pages 117--177
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo683}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2023
\vol 84
\pages 97--144
\crossref{https://doi.org/10.1090/mosc/353}
Citation in format AMSBIB
Contact us: