Facet defining inequalities among graph invariants: The system GraPHedron Original Research Article

We present a new computer system, called GraPHedron, which uses a polyhedral approach to help the user to discover optimal conjectures in graph theory. We define what should be optimal conjectures and propose a formal framework allowing to identify them. Here, graphs with n nodes are viewed as points in the Euclidian space, whose coordinates are the values of a set of graph invariants. To the convex hull of these points corresponds a finite set of linear inequalities. These inequalities computed for a few values of n can be possibly generalized automatically or interactively. They serve as conjectures which can be considered as optimal by geometrical arguments.