Isomorphism of weighted trees and Stanley's isomorphism conjecture for caterpillars

DOI10.4171/AIHPD/74zbMath1422.05054arXiv1405.4132OpenAlexW2900383210WikidataQ123164995 ScholiaQ123164995MaRDI QIDQ2327720

Jean-Sébastien Sereni, Martin Loebl

Publication date: 15 October 2019

Published in: Annales de l'Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.4132

zbMATH Keywords

treegraph isomorphismgraph reconstruction\(U\)-polynomial\(W\)-polynomialPotts partition functionStanley's isomorphism conjecture

Mathematics Subject Classification ID

Trees (05C05) Graph polynomials (05C31) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (14)

On the \(e\)-positivity of trees and spiders ⋮ A vertex-weighted Tutte symmetric function, and constructing graphs with equal chromatic symmetric function ⋮ A note on distinguishing trees with the chromatic symmetric function ⋮ Marked Graphs and the Chromatic Symmetric Function ⋮ Quasisymmetric functions distinguishing trees ⋮ A rooted variant of Stanley's chromatic symmetric function ⋮ A deletion-contraction relation for the chromatic symmetric function ⋮ On the smallest trees with the same restricted \(U\)-polynomial and the rooted \(U\)-polynomial ⋮ A tree distinguishing polynomial ⋮ Tutte polynomials for directed graphs ⋮ Extended chromatic symmetric functions and equality of ribbon Schur functions ⋮ Schur and \(e\)-positivity of trees and cut vertices ⋮ A few more trees the chromatic symmetric function can distinguish ⋮ The \(e\)-positivity and Schur positivity of some spiders and broom trees

Cites Work

• Unnamed Item
• Proper caterpillars are distinguished by their chromatic symmetric function
• Graphs with equal chromatic symmetric functions
• Chromatic polynomial, \(q\)-binomial counting and colored Jones function
• Intersection theory for graphs
• A weighted graph polynomial from chromatic invariants of knots
• Graph colorings and related symmetric functions: ideas and applications: A description of results, interesting applications, and notable open problems.
• A symmetric function generalization of the chromatic polynomial of a graph
• The Potts model and chromatic functions of graphs
• On distinguishing trees by their chromatic symmetric functions
• Graph Classes: A Survey

This page was built for publication: Isomorphism of weighted trees and Stanley's isomorphism conjecture for caterpillars