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- W4386160969 abstract "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." @default.
- W4386160969 created "2023-08-26" @default.
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- W4386160969 date "2023-08-24" @default.
- W4386160969 modified "2023-10-17" @default.
- W4386160969 title "Marked Graphs and the Chromatic Symmetric Function" @default.
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- W4386160969 doi "https://doi.org/10.1137/22m148046x" @default.
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