Abstract
A two-coloring of the vertices X of the hypergraph H=(X, ε) by red and blue has discrepancy d if d is the largest difference between the number of red and blue points in any edge. A two-coloring is an equipartition of H if it has discrepancy 0, i.e., every edge is exactly half red and half blue. Let f(n) be the fewest number of edges in an n-uniform hypergraph (all edges have size n) having positive discrepancy. Erdo{combining double acute accent}s and Sós asked: is f(n) unbounded? We answer this question in the affirmative and show that there exist constants c 1 and c 2 such that {Mathematical expression} where snd(x) is the least positive integer that does not divide x.
Original language | English (US) |
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Pages (from-to) | 151-160 |
Number of pages | 10 |
Journal | Combinatorica |
Volume | 7 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1987 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Computational Mathematics