Marked graphs and the chromatic symmetric function
The main result of this paper is the introduction of marked graphs and the marked graph polynomials ( -polynomial) associated with them. These polynomials can be defined via a deletion-contraction operation. These polynomials are a generalization of the -polynomial, introduced by Noble and Welsh, an...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/404830 |
| Acesso em linha: | https://hdl.handle.net/2117/404830 https://dx.doi.org/10.1137/22M148046X |
| Access Level: | acceso abierto |
| Palavra-chave: | Combinatorial analysis Graph theory Chromatic symmetric function Trees Chromatic basis Combinacions (Matemàtica) Grafs, Teoria de Classificació AMS::05 Combinatorics::05E Algebraic combinatorics Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Resumo: | The main result of this paper is the introduction of marked graphs and the marked graph polynomials ( -polynomial) associated with them. These polynomials can be defined via a deletion-contraction operation. These polynomials are a generalization of the -polynomial, introduced by Noble and Welsh, and a specialization of the -polynomial, introduced by Ellis-Monaghan and Moffatt. In addition, we describe an important specialization of the -polynomial, which we call the -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. |
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