Dean, Nathaniel2009-06-042009-06-042001Riggins, Kymberly Dawn. "On characterizing graphs with branchwidth at most four." (2001) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/17460">https://hdl.handle.net/1911/17460</a>.https://hdl.handle.net/1911/17460There are several ways in which we can characterize classes of graphs. One such way of classifying graphs is by their branchwidth. In working to characterize the class of graphs with branchwidth at most four beta 4 we have found a set of reductions that reduces members of beta 4 to the zero graph. We have also computed several planar members of the obstruction set Ob4 for graphs with branchwidth at most four. This thesis will summarize previous results on branchwidth and reveal the previously mentioned new results.43 p.application/pdfengCopyright 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.MathematicsOperations researchThesisTHESIS MATH.SCI. 2001 RIGGINS