Örün, Onur Muharrem2016-07-122016-07-122016-062016-062016-06-22http://hdl.handle.net/11693/30129Cataloged from PDF version of article.Thesis (M.S.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2016.Includes bibliographical references (leaves 55-56).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.vii, 56 leaves : charts.Englishinfo:eu-repo/semantics/openAccessGroebner basisHilbert's NullstellensatzGraph colorabilityHamiltonian cyclePlanar graphEdge-chromatic numberThesisB153612