Chromatic Polynomial

The chromatic polynomial is a function used in algebraic graph theory that counts how many ways a graph can be properly colored using a given number of colors. For a graph G, its value at a whole number k gives the exact count of proper colorings that use k colors, and there is one polynomial in x that matches this count at every non-negative whole number k. George David Birkhoff introduced the idea in 1912 while studying the four color problem for planar graphs, and Hassler Whitney extended it to graphs in general in 1932. The chromatic polynomial was later connected to the Tutte polynomial and to the Potts model from statistical physics, and it remains a central object for studying how a graph colorability relates to the roots of a polynomial.