The so-called strong perfect graph conjecture (SPGC) might enable mathematicians to quickly identify perfect graphs, which have properties that make otherwise intractable problems involving networks easy to solve. Now if four graph theorists9 proof of the SPGC holds up, they will reap a $10,000 bounty.

Let G denote a finite simple graph with edge ideal I(G). Letting I(G)∨ denote the Alexander dual of I(G), we show that a description of the induced cycles of G of odd length is encoded in the… Expand

Let G be a finite simple graph with edge ideal I(G). Let I(G)∨ denote the Alexander dual of I(G). We show that a description of all induced cycles of odd length in G is encoded in the associated… Expand

This dissertation develops novel approaches to solving computationally difficult combinatorial optimization problems on graphs, namely maximum independent set, maximum clique, graph coloring, minimum… Expand