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The chromatic polynomial of an unlabeled graph

✍ Scribed by P Hanlon


Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
615 KB
Volume
38
Category
Article
ISSN
0095-8956

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## Abstract In this paper we obtain chromatic polynomials of connected 3‐ and 4‐chromatic planar graphs that are maximal for positive integer‐valued arguments. We also characterize the class of connected 3‐chromatic graphs having the maximum number of __p__‐colorings for __p__ β‰₯ 3, thus extending a

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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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✍ Norman Biggs πŸ“‚ Article πŸ“… 1973 πŸ› Elsevier Science 🌐 English βš– 739 KB

The chromatic polynomial ;X chromial) of a graph was first defined by Birkhoff in 1912, ;md gives the number of ways or" properly colov iing the vertices of the graph with any number of colours. A good survey of the b-sic facts about these polynomials may be found in the article by Read [ 3 3 . It