Results 1 to 10 of about 2,074 (148)
A categorification of the chromatic symmetric polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Stanley chromatic polynomial of a graph $G$ is a symmetric function generalization of the chromatic polynomial, and has interesting combinatorial properties.
Radmila Sazdanović, Martha Yip
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Marked Graphs and the Chromatic Symmetric Function [PDF]
SIAM Journal on Discrete Mathematics, 2023 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 $\mathbf{V}$-polynomial ...
JOSÉ Aliste-Prieto +2 more
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A Complete Multipartite Basis for the Chromatic Symmetric Function [PDF]
SIAM Journal on Discrete Mathematics, 2021 Accepted manuscript; see DOI for journal ...
Logan Crew, Sophie Spirkl
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On distinguishing trees by their chromatic symmetric functions [PDF]
Journal of Combinatorial Theory - Series A, 2008 Let $T$ be an unrooted tree. The \emph{chromatic symmetric function} $X_T$, introduced by Stanley, is a sum of monomial symmetric functions corresponding to proper colorings of $T$. The \emph{subtree polynomial} $S_T$, first considered under a different name by Chaudhary and Gordon, is the bivariate generating function for subtrees of $T$ by their ...
Jeremy L Martin
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Combinatorial reciprocity for the chromatic polynomial and the chromatic symmetric function
Discrete Mathematics, 2020 minor ...
Olivier Bernardi, Philippe Nadeau
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A note on distinguishing trees with the chromatic symmetric function [PDF]
Discrete Mathematics, 2022 For a tree $T$, consider its smallest subtree $T^{\circ}$ containing all vertices of degree at least $3$. Then the remaining edges of $T$ lie on disjoint paths each with one endpoint on $T^{\circ}$. We show that the chromatic symmetric function of $T$ determines the size of $T^{\circ}$, and the multiset of the lengths of these incident paths.
Logan Crew
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Graphs with equal chromatic symmetric functions
Discrete Mathematics, 2014 Stanley [9] introduced the chromatic symmetric function ${\bf X}_G$ associated to a simple graph $G$ as a generalization of the chromatic polynomial of $G$. In this paper we present a novel technique to write ${\bf X}_G$ as a linear combination of chromatic symmetric functions of smaller graphs.
Rosa Orellana
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Chromatic symmetric functions from the modular law [PDF]
Journal of Combinatorial Theory - Series A, 2021 In this article we show how to compute the chromatic quasisymmetric function of indifference graphs from the modular law introduced by Guay-Paquet. We provide an algorithm which works for any function that satisfies this law, such as unicellular LLT polynomials.
Alex Abreu, Antonio Nigro
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The Chromatic Symmetric Functions of Trivially Perfect Graphs and Cographs [PDF]
Graphs and Combinatorics, 2018 Richard P. Stanley defined the chromatic symmetric function of a simple graph and has conjectured that every tree is determined by its chromatic symmetric function. Recently, Takahiro Hasebe and the author proved that the order quasisymmetric functions, which are analogs of the chromatic symmetric functions, distinguish rooted trees.
Shuhei Tsujie
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Proper caterpillars are distinguished by their chromatic symmetric function
Discrete Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
JOSÉ Aliste-Prieto, JOSÉ Zamora
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