... chromatic number, although we phrase it only for chromatic number In the next section we present the lower bound in Theorem and the rest of the paper is devoted to the proof of the upper bound The ... coloring of a k-graph is a coloring of its vertices such that no edge is monochromatic, and the chromatic number is the minimum number of colors in a proper coloring An easy consequence of the Local ... one of these colors, the probability of the event Ae , that an edge e is monochromatic, is at most 1/9∆ Moreover Ae is independent of all other events Af unless |f ∩ e| > 0, and the number of...