Computing Chromatic Polynomials of Large Graphs \(I\)

An efficient algorithm for calculating the chromatic polynomial of large graphs relative to the tree basis is presented. As an application of this algorithm, the degree thirty-two chromatic polynomial of the dual of the truncated icosahedron is calculated. Before this algorithm, only the by-hand calculations of Hall, Siry, and Vander-slice, completed in 1965, had produced this chromatic polynomial.