I’ve spent several days at a Canadian conference (CanaDAM) talking to fellow researchers about different things. I’ll post some of these ideas to the blog.
Wendy Myrvold suggests that we use this approach on other graph classes of interest where the independence number is hard to compute but there is more structure, for instance, cubic graphs, and see if anything interesting pops out. She also suggests trying to characterize graphs where independence number equals clique covering number, and idea that Scheinerman had also suggested to us. This class of graphs includes the graphs where independence number equlas Lovasz’ theta.