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Chromatic Polynomials and the Symmetric Group

✍ Scribed by Philippe Pitteloud

Book ID: 106047489
Publisher: Springer Japan
Year: 2004
Tongue: English
Weight: 327 KB
Volume: 20
Category: Article
ISSN: 0911-0119
DOI: 10.1007/s00373-003-0544-x

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📜 SIMILAR VOLUMES

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✍ Wakelin, C. D. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 827 KB

In this paper we present some results on the sequence of coefficients of the chromatic polynomial of a graph relative to the complete graph basis, that is, when it is expressed as the sum of the chromatic polynomials of complete graphs. These coefficients are the coefficients of what is often called

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✍ R.P. Stanley 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 932 KB

For a finite graph \(G\) with \(d\) vertices we define a homogeneous symmetric function \(X_{4 ;}\) of degree \(d\) in the variables \(x_{1}, x_{2}, \ldots\). If we set \(x_{1}=\cdots=x_{n}=1\) and all other \(x_{t}=0\), then we obtain \(Z_{1}(n)\), the chromatic polynomial of (; evaluated at \(n\).

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✍ F. M. Dong 📂 Library 📅 2005 🏛 World Scientific 🌐 English ⚖ 9 MB

This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials. Dividing the book into three main parts, the authors take readers from the rudiments of chromatic polynomials to more com

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✍ Earl Glen Whitehead Jr.; Lian-Chang Zhao 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 303 KB

## Abstract We prove that the multiplicity of the root 1 in the chromatic polynomial of a simple graph __G__ is equal to the number of nontrivial blocks in __G__. In particular, a connected simple graph __G__ has a cutpoint if and only if its chromatic polynomial is divisible by (λ – 1)^2^. We appl

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