Dataset for "A Computational Search for Minimal Obstruction Graphs for the Lovász-Schrijver SDP Hierarchy"

This dataset contains supporting materials for our research manuscript "A Computational Search for Minimal Obstruction Graphs for the Lovász-Schrijver SDP Hierarchy". Below you'll find the following files: LS_+ certificate packages.zip, LS_+^2 certificate packages.zip, and LS_+^3 certificate packages.zip respectively contains all LS_+, LS_+^2, and LS_+^3 certificate packages mentioned in the manuscript. Code.zip contains MATLAB code for verifying all LS_+, LS_+^2, and LS_+^3 certificate packages in this dataset. List of 4-minimal graphs.zip contains a list of the 4107 4-minimal graphs we discovered, in graph6 format. Tables of graphs.zip contains lists of graphs mentioned in Figure 8 and Tables 1, 2, and 3 in the manuscript, in graph6 format. Each of the above zipped folders also contains a readme.txt file which provides more details about the contents of that folder.