Linear Versus Hereditary Discrepancy*

Abstract

Lovasz, Spencer and Vesztergombi proved that the linear discrepancy of a hypergraph H is bounded above by the hereditary discrepancy of H, and conjectured a sharper bound that involves the number of vertices in H. In this paper we give a short proof of this conjecture for hypergraphs of hereditary discrepancy 1. For hypergraphs of higher hereditary discrepancy we give some partial results and propose a sharpening of the conjecture.