Being a https://en.wikipedia.org/wiki/Perfect_graph https://en.wikipedia.org/wiki/Perfect_graph is not monotonic under adding edges, and it's certainly an inter

Being a https://en.wikipedia.org/wiki/Perfect_graph https://en.wikipedia.org/wiki/Perfect_graph is not monotonic under adding edges, and it's certainly an interesting property for a graph to have! (But yes, most interesting properties are monotonic under adding edges)