As an aside, theres some really beautiful results in graph theory that are only nicely expressible if you use linear algebra (aka spectral graph theory). That

As an aside, theres some really beautiful results in graph theory that are only nicely expressible if you use linear algebra (aka spectral graph theory). That being said, there are several problems with the paper: 1) it seems to implicitly assuming (without realizing it) that any two graphs it is considering at k-regular for some unspecified k. This is barely more general than assuming that graphs are planar, so itd be easy to have pretty reasonable algorithm for such a case (i'm pretty sure there are bunches in the research literature). Also, it doesn't really seem to be addressing integrality of the linear programs, which i think is kinda key when using linear programs for combinatorics!