Isomorphism of weighted trees and Stanley's isomorphism conjecture for caterpillars
Martin Loebl
Charles University, Prague, CzechiaJean-Sébastien Sereni
Centre National de la Recherche Scientifique, Strasbourg, France
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Abstract
This paper contributes to a programme initiated by the first author: "How much information about a graph is revealed in its Potts partition function?“ We show that the -polynomial distinguishes non-isomorphic weighted trees of a good family. The framework developed to do so also allows us to show that the -polynomial distinguishes non-isomorphic caterpillars. This establishes Stanley's conjecture for caterpillars, an extensively studied problem.
Cite this article
Martin Loebl, Jean-Sébastien Sereni, Isomorphism of weighted trees and Stanley's isomorphism conjecture for caterpillars. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), no. 3, pp. 357–384
DOI 10.4171/AIHPD/74