Linear Versus Hereditary Discrepancy
نویسندگان
چکیده
Lovász, 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.
منابع مشابه
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The Discrepancy of a hypergraph is the minimum attainable value, over twocolorings of its vertices, of the maximum absolute imbalance of any hyperedge. The Hereditary Discrepancy of a hypergraph, defined as the maximum discrepancy of a restriction of the hypergraph to a subset of its vertices, is a measure of its complexity. Lovász, Spencer and Vesztergombi (1986) related the natural extension ...
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ورودعنوان ژورنال:
- Combinatorica
دوره 25 شماره
صفحات -
تاریخ انتشار 2004