Classes of graphs with \(e\)-positive chromatic symmetric function

zbMath1420.05177arXiv1808.03391MaRDI QIDQ2325752

Owen Merkel, Angèle M. Foley, Chính T. Hoàng

Publication date: 30 September 2019

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.03391

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Structural characterization of families of graphs (05C75) Coloring of graphs and hypergraphs (05C15)

Related Items (16)

On the \(e\)-positivity of trees and spiders ⋮ A combinatorial expansion of vertical-strip LLT polynomials in the basis of elementary symmetric functions ⋮ Plethysms of chromatic and Tutte symmetric functions ⋮ A vertex-weighted Tutte symmetric function, and constructing graphs with equal chromatic symmetric function ⋮ A combinatorial formula for the Schur coefficients of chromatic symmetric functions ⋮ A deletion-contraction relation for the chromatic symmetric function ⋮ The \(e\)-positivity of two classes of cycle-chord graphs ⋮ Chromatic symmetric functions and \(H\)-free graphs ⋮ Chromatic symmetric functions in noncommuting variables revisited ⋮ On the \(e\)-positivity of \((claw, 2K_2)\)-free graphs ⋮ Melting lollipop chromatic quasisymmetric functions and Schur expansion of unicellular LLT polynomials ⋮ Schur and \(e\)-positivity of trees and cut vertices ⋮ Modular relations of the Tutte symmetric function ⋮ The twinning operation on graphs does not always preserve \(e\)-positivity ⋮ A Complete Multipartite Basis for the Chromatic Symmetric Function ⋮ The \(e\)-positivity and Schur positivity of some spiders and broom trees

Cites Work

• Unnamed Item
• Unnamed Item
• Chromatic quasisymmetric functions
• Chromatic classical symmetric functions
• Resolving Stanley's \(e\)-positivity of claw-contractible-free graphs
• Graph colorings and related symmetric functions: ideas and applications: A description of results, interesting applications, and notable open problems.
• On claw-free asteroidal triple-free graphs
• The chromatic symmetric functions of trivially perfect graphs and cographs
• On immanants of Jacobi-Trudi matrices and permutations with restricted position
• A symmetric function generalization of the chromatic polynomial of a graph
• Chromatic symmetric functions and \(H\)-free graphs
• The Roberts characterization of proper and unit interval graphs
• On \(e\)-positivity and \(e\)-unimodality of chromatic quasisymmetric functions
• Representation of a finite graph by a set of intervals on the real line
• Approximating the Bandwidth for Asteroidal Triple-Free Graphs
• On the Co-P₃ -Structure of Perfect Graphs
• The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture
• A chromatic symmetric function in noncommuting variables

This page was built for publication: Classes of graphs with \(e\)-positive chromatic symmetric function