# 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…

## 71 Citations

Problems on chromatic polynomials of hypergraphs

- MathematicsElectron. J. Graph Theory Appl.
- 2020

This short article will focus on introducing some important open prblems on chromatic polynomials of hypergraphs.

Note on chromatic polynomials of the threshold graphs

- MathematicsElectron. J. Graph Theory Appl.
- 2019

This paper gives a formula relating the chromatic polynomial of Ḡ (the complement of G ) to the chromatics polynomorphism of G in terms of the generalized Bell polynomials.

Recursion Relations for Chromatic Coefficients for Graphs and Hypergraphs

- MathematicsDiscuss. Math. Graph Theory
- 2022

A generalization of Whitney’s broken cycle theorem for hypergraphs is provided, as well as deriving an explicit formula for the linear coefficient of the chromatic polynomial of the r-complete hypergraph in terms of roots of the Taylor polynomials for the exponential function.

An introduction to the k-defect polynomials

- Mathematics
- 2019

Abstract The 0-defect polynomial of a graph is just the chromatic polynomial. This polynomial has been widely studied in the literature. Yet little is known about the properties of k-defect…

The Orbital Chromatic Polynomial of a Cycle

- Mathematics
- 2020

The orbital chromatic polynomial introduced by Cameron and Kayibi counts the number of proper $\lambda$-colorings of a graph modulo a group of symmetries. In this paper, we establish expansions for…

ON COLOURABILITY OF HYPERGRAPHS

- Mathematics
- 2020

This article encompasses around the concept of colourability in hypergraphs. The deletion-contraction attribute frequently observed in 2-graph has also come in connection with hypergraphs leading to…

Properties of chromatic polynomials of hypergraphs not held for chromatic polynomials of graphs

- MathematicsEur. J. Comb.
- 2017

The Amazing Chromatic Polynomial

- MathematicsThe Mathematical Intelligencer
- 2022

Let G be a combinatorial graph with vertices V and edges E. A proper coloring of G is an assignment of colors to the vertices such that no edge connects two vertices of the same color. These are the…

Chromatic Polynomials of Oriented Graphs

- MathematicsElectron. J. Comb.
- 2019

It is found that oriented graphs which have chromatic polynomials can be both identified and constructed in polynomial time as they are exactly the family of quasi-transitive oriented co-interval graphs.

Chromatic polynomials of 2-edge coloured graphs

- Mathematics
- 2020

Using the definition of colouring of $2$-edge-coloured graphs derived from $2$-edge-coloured graph homomorphism, we extend the definition of chromatic polynomial to $2$-edge-coloured graphs. We find…

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