Graph Theory Uncovers the Roots of Perfection
@article{Mackenzie2002GraphTU,
title={Graph Theory Uncovers the Roots of Perfection},
author={Dana Mackenzie},
journal={Science},
year={2002},
volume={297},
pages={38 - 38}
}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.
4 Citations
Algebraic methods for detecting odd holes in a graph
- Mathematics
- 2008
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…
Associated primes of monomial ideals and odd holes in graphs
- Mathematics
- 2008
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…
Maximum independent set and related problems, with applications
- Computer Science
- 2003
This dissertation develops novel approaches to solving computationally difficult combinatorial optimization problems on graphs, namely maximum independent set, maximum clique, graph coloring, minimum…