Show simple item record

dc.contributor.authorRomero Barbosa, Julian 18:27:42 (GMT) 18:27:42 (GMT)
dc.description.abstractVarious feasibility problems in Combinatorial Optimization can be stated using systems of polynomial equations. Determining the existence of a \textit{stable set} of a given size, finding the \textit{chromatic number} of a graph or more generally, determining the feasibility of an \textit{Integer Programming problem} are classical examples of this. In this thesis we study a powerful tool from Algebraic Geometry, called \textit{Hilbert's Nullstellensatz}. It characterizes the \textit{infeasibility} of a system of polynomial equations by the \textit{feasibility} of a possibly very large system of \textit{linear equations}. The solutions to this linear system provide \textit{certificates} for the infeasibility of the polynomial system, called \textit{Nullstellensatz Certificates}. In this thesis we focus on the study of Nullstellensatz Certificates for the existence of \textit{proper colorings} of graphs. We use basic ideas from \textit{duality theory} to determine various properties of the Nullstellensatz Certificates. We give new proofs to several known results in the current literature and present some new results that shed some light on the relationship between the sparsity of a graph and the \textit{size} of the Nullstellensatz Certificates for \textit{$k$-colorability}.en
dc.publisherUniversity of Waterlooen
dc.subjectAlgebraic Geometryen
dc.subjectCombinatorial Optimizationen
dc.subjectHilbert's Nullstellensatzen
dc.subjectGraph Coloringen
dc.subjectGraph Theoryen
dc.titleApplied Hilbert's Nullstellensatz for Combinatorial Problemsen
dc.typeMaster Thesisen
dc.pendingfalse and Optimizationen and Optimizationen of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorTunçel, Levent
uws.contributor.affiliation1Faculty of Mathematicsen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages