Extremal Problems in Coloring and Labeling of Graphs and Partial Orders

Abstract

The fractional weak discrepancy of a poset P, written wdF(P) is the least k such that there is a labeling f of P such that f(y) -- f(x) ≥ 1 when x ≺ y and |f(y) -- f(x)| ≤ k when x and y are incomparable in P. We give a complete description of the forbidden subposets for the property wdF( P) ≤ k when k is an integer.