Williams, Aaron2006-08-222006-08-2220042004http://hdl.handle.net/10012/1024Edmonds and Giles conjectured that the maximum number of directed joins in a packing is equal to the minimum weight of a directed cut, for any weighted directed graph. This is a generalization of Woodall's Conjecture (which is still open). Schrijver found the first known counterexample to the Edmonds-Giles Conjecture, while Cornuejols and Guenin found the next two. In this thesis we introduce new counterexamples, and prove that all minimal counterexamples of a certain type have now been found.application/pdf1797821 bytesapplication/pdfenCopyright: 2004, Williams, Aaron. All rights reserved.Mathematicsdirected graphdirected cutdirected joinmin-maxWoodall's ConjectureEdmonds-Giles ConjectureMaster Thesis