MARKED GRAPHS AND THE CHROMATIC SYMMETRIC FUNCTION

Jose Aliste-Prieto, Anna De Mier, Rosa Orellana, Jose Zamora

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The main result of this paper is the introduction of marked graphs and the marked graph polynomials (M-polynomial) associated with them. These polynomials can be defined via a deletion-contraction operation. These polynomials are a generalization of the W-polynomial, introduced by Noble and Welsh, and a specialization of the V-polynomial, introduced by Ellis-Monaghan and Moffatt. In addition, we describe an important specialization of the M-polynomial, which we call the D-polynomial. Furthermore, we present an efficient algorithm for computing the chromatic symmetric function of a graph in the star basis of symmetric functions. As an application of these tools, we prove that proper trees of diameter at most 5 are reconstructible from its chromatic symmetric function.

Original languageEnglish
Pages (from-to)1881-1919
Number of pages39
JournalSIAM Journal on Discrete Mathematics
Volume37
Issue number3
DOIs
Publication statusPublished - 2023

Keywords

  • chromatic basis
  • chromatic symmetric function
  • trees

ASJC Scopus subject areas

  • Mathematics(all)

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