Exact Graph Coloring Using Inclusion-Exclusion
Years and Authors of Summarized Original Work
2006; Björklund, Husfeldt
A k-coloring of a graph G = (V, E) assigns one of k colors to each vertex such that neighboring vertices have different colors. This is sometimes called vertex coloring.
The smallest integer k for which the graph G admits a k-coloring is denoted χ(G) and called the chromatic number. The number of k-colorings of G is denoted P(G; k) and called the chromatic polynomial.
The central observation is that χ(G) and P(G; k) can be expressed by an inclusion-exclusion formula whose terms are determined by the number of independent sets of induced subgraphs of G. For \(X \subseteq V\)
- 2.Björklund A, Husfeldt T, Kaski P, Koivisto M (2007) Fourier meets Möbius: fast subset convolution. In: Proceedings of the 39th annual ACM symposium on theory of computing (STOC), San Diego, 11–13 June 2007. Association for Computing Machinery, New York, pp 67–74Google Scholar