On four colored sets with nondecreasing diameter and the erdos-ginzburg-Ziv theorem


A set X, with a coloring Δ: X → ℤm, is zero-sum if ∑x∈X Δ(x) = 0. Let f(m, r) (let fzs(m, 2r)) be the least N such that for every coloring of 1,⋯, N with r colors (with elements from r disjoint copies of ℤm) there exist monochromatic (zero-sum) m-element subsets B1 and B2, not necessarily the same color, such that (a) max(B1) - min(B1)≤max(B2) - min(B2), and (b) max(B1)

Publication Title

Journal of Combinatorial Theory. Series A