  


Linear inequalities among graph invariants: using GraPHedron to uncover optimal relationships
Julie Christophe (juchristulb.ac.be) Abstract: Optimality of a linear inequality in finitely many graph invariants is defined through a geometric approach. For a fixed number of graph nodes, consider all the tuples of values taken by the invariants on a selected class of graphs. Then form the polytope which is the convex hull of all these tuples. By definition, the optimal linear inequalities correspond to the facets of this polytope. They are finite in number, are logically independent, and generate precisely all the linear inequalities valid on the class of graphs. The computer system GraPHedron, developed by some of the authors, is able to produce experimental data about such inequalities for a Keywords: Graph invariants, polytope, optimal linear inequalities, GraPHedron Category 1: Other Topics (Other ) Citation: Submitted in Augustus 2004 Download: [PDF] Entry Submitted: 09/21/2004 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  