Efficient Computation of Chromatic and Flow Polynomials

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dc.contributor.advisorHicks, Illya V
dc.creatorBrimkov, Boris
dc.date.accessioned2017-07-31T14:26:47Z
dc.date.available2017-07-31T14:26:47Z
dc.date.created2015-12
dc.date.issued2015-10-13
dc.date.submittedDecember 2015
dc.date.updated2017-07-31T14:26:47Z
dc.description.abstractThis thesis surveys chromatic and flow polynomials, and presents new efficient methods to compute these polynomials on specific families of graphs. The chromatic and flow polynomials of a graph count the number of ways to color and assign flow to the graph; they also contain other important information such as the graph's chromatic number, Hamiltonicity, and number of acyclic orientations. Unfortunately, these graph polynomials are generally difficult to compute; thus, research in this area often focuses on exploiting the structure of specific families of graphs in order to characterize their chromatic and flow polynomials. In this thesis, I present closed formulas and polynomial-time algorithms for computing the chromatic polynomials of novel generalizations of trees, cliques, and cycles; I also use graph duality to compute the flow polynomials of outerplanar graphs and generalized wheel graphs. The proposed methods are validated by computational results.
dc.format.mimetypeapplication/pdf
dc.identifier.citationBrimkov, Boris. "Efficient Computation of Chromatic and Flow Polynomials." (2015) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/95530">https://hdl.handle.net/1911/95530</a>.
dc.identifier.urihttps://hdl.handle.net/1911/95530
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectChromatic polynomial
dc.subjectflow polynomial
dc.titleEfficient Computation of Chromatic and Flow Polynomials
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
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