• Corpus ID: 52064991

An Introduction to Chromatic Polynomials

@inproceedings{Zhang2018AnIT,
  title={An Introduction to Chromatic Polynomials},
  author={Julie Zhang},
  year={2018}
}
This paper will provide an introduction to chromatic polynomials. We will first define chromatic polynomials and related terms, and then derive important properties. Once the basics have been established, we will explore applications and theorems related to chromatic polynomials, and introduce the idea of chromatic polynomials associated with hypergraphs and chromatic polynomials associated with fractional graph colouring. To conclude the paper, we will discuss some unsolved graph theory… 

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References

SHOWING 1-3 OF 3 REFERENCES
Fractional Graph Theory: A Rational Approach to the Theory of Graphs
General Theory: Hypergraphs. Fractional Matching. Fractional Coloring. Fractional Edge Coloring. Fractional Arboricity and Matroid Methods. Fractional Isomorphism. Fractional Odds and Ends. Appendix.