Note on Nordhaus-Gaddum Problems for Colin de Verdière type Parameters

We establish the bounds 4 3 6 b 6 b 6 p 2, where b and b are the Nordhaus-Gaddum sum upper bound multipliers, i.e., (G)+(G) 6 bjGj and (G)+(G) 6 bjGj for all graphs G, and and are Colin de Verdiere type graph parameters. The Nordhaus-Gaddum sum lower bound for and is conjectured to be jGj 2, and if these parameters are replaced by the maximum nullity M(G), this bound is called the Graph Complement Conjecture in the study of minimum rank/maximum nullity problems.This article is published as Barrett, Wayne, Shaun M. Fallat, H. Tracy Hall, and Leslie Hogben. "Note on Nordhaus-Gaddum Problems for Colin de Verdière type Parameters." The Electronic Journal of Combinatorics 20, no. 3 (2013): P56. DOI: 10.37236/2570. Posted with permission.</p

Note on Nordhaus-Gaddum Problems for Colin de Verdière type Parameters

We establish the bounds 4 3 6 b 6 b 6 p 2, where b and b are the Nordhaus-Gaddum sum upper bound multipliers, i.e., (G)+(G) 6 bjGj and (G)+(G) 6 bjGj for all graphs G, and and are Colin de Verdiere type graph parameters. The Nordhaus-Gaddum sum lower bound for and is conjectured to be jGj 2, and if these parameters are replaced by the maximum nullity M(G), this bound is called the Graph Complement Conjecture in the study of minimum rank/maximum nullity problems