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Graphs with equal chromatic symmetric functions

✍ Scribed by Orellana, Rosa; Scott, Geoffrey

Book ID
122179718
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
526 KB
Volume
320
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES

A Symmetric Function Generalization of t
A Symmetric Function Generalization of the Chromatic Polynomial of a Graph
✍ R.P. Stanley πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 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 \(n\).

Graphs whose choice number is equal to t
Graphs whose choice number is equal to their chromatic number
✍ Gravier, Sylvain; Maffray, FrοΏ½dοΏ½ric πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 219 KB

A graph G is k-choosable if it admits a vertex-coloring whenever the colors allowed at each vertex are restricted to a list of length k. If Ο‡ denotes the usual chromatic number of G, we are interested in which kind of G is Ο‡-choosable. This question contains a famous conjecture, which states that ev