%0 Journal Article
%T Gr£¿bner Basis Convex Polytopes and Planar Graph
%A Dang Vu Giang
%J Mathematics
%D 2012
%I arXiv
%X Using the Gr\"obner basis of an ideal generated by a family of polynomials we prove that every planar graph is 4-colorable. Here we also use the fact that the complete graph of 5 vertices is not included in any planar graph.
%U http://arxiv.org/abs/1202.4510v1