Groebner basis approach in graph-theoretical problems

Abstract

In the study of graphs, it is often desirable to know about the colorability properties of a given graph or whether it is planar or if it contains a Hamiltonian cycle. We consider such problems and describe corresponding encodings to equate these problems to problems of solving systems of polynomial equations. This in turn reduces the problem to computing lead term ideals from a certain generating set using Groebner basis theory.