History
George David Birkhoff introduced the chromatic polynomial in 1912, defining it only for planar graphs, in an attempt to prove the four color theorem. If denotes the number of proper colorings of with colors then one could establish the four color theorem by showing for all planar graphs . In this way he hoped to apply the powerful tools of analysis and algebra for studying the roots of polynomials to the combinatorial coloring problem.
Hassler Whitney generalised Birkhoff’s polynomial from the planar case to general graphs in 1932. In 1968 Read asked which polynomials are the chromatic polynomials of some graph, a question that remains open, and introduced the concept of chromatically equivalent graphs. Today, chromatic polynomials are one of the central objects of algebraic graph theory
Read more about this topic: Chromatic Polynomial
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