- Volume 15 Issue 1
In this paper, we introduce the arrangement of hyperplanes and the graph theory. In particular, we explain how to study the 4-color problem by using characteristic polynomials of the arrangement of hyperplanes. The 4-color problem was appeared in 1852 at first and Appel and Haken proved it by using computer in 1976. The arrangement of hyperplanes induced from a graph is called a graphic arrangement. Graphic arrangement is a subarrangement of Braid arrangement. Thus the chromatic function of a graph is equal to the characteristic polynomial of a graphic arrangement. If we use this result, we can apply the theory of the arrangement of hyperplanes to the study for the chromatic functions.
- Graph Theory; A Development from the 4-Color Problem Aigner, Martin
- Graph Theory with Applications Bondy, J.A.;U. S. R. Murty
- Arrangements of Hyperplanes Orlik, Peter;Hiroaki Terao
- Introduction to Graph Theory West, Douglas B.