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.

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.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/74
Classification : 05-XX
Mots-clés : W-polynomial, tree, graph reconstruction, graph isomorphism, U-polynomial, Stanley’s isomorphism conjecture, Potts partition function 
@article{AIHPD_2019__6_3_357_0,
     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 = {https://www.numdam.org/articles/10.4171/aihpd/74/}
}
TY  - JOUR
AU  - Loebl, Martin
AU  - Sereni, Jean-Sébastien
TI  - Isomorphism of weighted trees and Stanley's isomorphism conjecture for caterpillars
JO  - Annales de l’Institut Henri Poincaré D
PY  - 2019
SP  - 357
EP  - 384
VL  - 6
IS  - 3
UR  - https://www.numdam.org/articles/10.4171/aihpd/74/
DO  - 10.4171/aihpd/74
LA  - en
ID  - AIHPD_2019__6_3_357_0
ER  - 
%0 Journal Article
%A Loebl, Martin
%A Sereni, Jean-Sébastien
%T Isomorphism of weighted trees and Stanley's isomorphism conjecture for caterpillars
%J Annales de l’Institut Henri Poincaré D
%D 2019
%P 357-384
%V 6
%N 3
%U https://www.numdam.org/articles/10.4171/aihpd/74/
%R 10.4171/aihpd/74
%G en
%F AIHPD_2019__6_3_357_0
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. https://www.numdam.org/articles/10.4171/aihpd/74/

Cité par Sources :