Geodesic
Isomorphism of weighted trees and Stanley's isomorphism conjecture for caterpillars
Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 3, pp. 357-384

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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 W-polynomial distinguishes non-isomorphic weighted trees of a good family. The framework developed to do so also allows us to show that the W-polynomial distinguishes non-isomorphic caterpillars. This establishes Stanley's conjecture for caterpillars, an extensively studied problem.

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Publié le :
DOI : 10.4171/aihpd/74
Classification : 05-XX
Keywords: $W$-polynomial, tree, graph reconstruction, graph isomorphism, $U$-polynomial, Stanley’s isomorphism conjecture, Potts partition function 
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     author = {Loebl, Martin and Sereni, Jean-S\'ebastien},
     title = {Isomorphism of weighted trees and {Stanley's} isomorphism conjecture for caterpillars},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {357--384},
     volume = {6},
     number = {3},
     year = {2019},
     doi = {10.4171/aihpd/74},
     mrnumber = {4002670},
     zbl = {1422.05054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpd/74/}
}
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Loebl, Martin; Sereni, Jean-Sébastien. Isomorphism of weighted trees and Stanley's isomorphism conjecture for caterpillars. Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 3, pp. 357-384. doi: 10.4171/aihpd/74

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