Complete Minors and Independence Number

Let G be a graph with n vertices and independence number . Hadwiger's conjecture implies that G contains a clique minor of order at least n/. In 1982, Duchet and Meyniel proved that this bound holds within a factor 2. Our main result gives the first improvement on their bound by an absolute constant factor. We show that G contains a clique minor of order larger than .504n/. We also prove related results giving lower bounds on the order of the largest clique minor.

• Type: Journal
• Year: 2010
• Where: SIAMDM
• Authors: Jacob Fox
• Keywords: Absolute Constant Factor, Clique, Independence Number, SIAMDM 2010