We bound the hereditary discrepancy of a hypergraph H in two colors in terms of its hereditary discrepancy in c colors. We show that herdisc(H, 2) ≤ Kcherdisc(H, c), where K is some absolute constant. This bound is sharp.

We show that a proper coloring of the diagram of an interval order I may require 1 + I-log 2 height(l)] colors and that 2 + l-log 2 height(I)'] colors always suffice. For the proof of the upper bound we use the following fact: A sequence C 1 ..... C h of sets (of colors) with the property (ct) C ~ C i _ l U C i for all l < i < j ~ < h can be used to color the diagram of an interval order with t...

We show that a proper coloring of the diagram of an interval order I may require 1 + dlog 2 height(I) e colors and that 2 + dlog 2 height(I) e colors always suuce. For the proof of the upper bound we use the following fact: A sequence C 1 ; : : : ; C h of sets (of colors) with the property () C j 6 6 C i?1 C i for all 1 < i < j h. can be used to color the diagram of an interval order with the c...

The Sloan Digital Sky Survey provides colors for more than 100,000 moving objects, among which a significant fraction has albedos determined. Here we combined and albedo in order to perform cluster analysis on the main-belt asteroid population, identify C-cluster, group of related C-type as defined earlier work. Members this C-cluster are fair agreement with color boundaries B DeMeo Carry (2013...

A k?coloring of an oriented graph G = (V; A) is an assignment c of one of the colors 1; 2; : : :; k to each vertex of the graph such that, for every arc (x; y) of G, c(x) 6 = c(y). The k?coloring is good if for every arc (x; y) of G there is no arc (z; t) 2 A such that c(x) = c(t) and c(y) = c(z). A k?coloring is said to be semi?strong if for every vertex x of G, c(z) 6 = c(t) for any pair fz; ...

Mastermind is a famous two-player game, where the codemaker has to choose a secret code and the codebreaker has to guess it in as few questions as possible. The code consists of 4 pegs, each of which is one of 6 colors. In Generalized Mastermind a general number p of pegs and a general number c of colors is considered. Let f(p, c) be the pessimistic number of questions for the generalization of...

In this article we introduce combinatorial multi-color discrepancies and generalize several classical results from 2–color discrepancy theory to c colors (c ≥ 2). We give a recursive method that constructs c–colorings from approximations of 2–color discrepancies. This method works for a large class of theorems like the ‘six standard deviations’ theorem of Spencer, the Beck–Fiala theorem, the re...

Suppose that n > (log k), where c is a fixed positive constant. We prove that no matter how the edges of Kn are colored with k colors, there is a copy of K4 whose edges receive at most two colors. This improves the previous best bound of k k, where c′ is a fixed positive constant, which follows from results on classical Ramsey numbers.

We call the digraph D an m-colored digraph if the arcs of D are colored with m colors. A path (or a cycle) is called monochromatic if all of its arcs are colored alike. A cycle is called a quasi-monochromatic cycle if with at most one exception all of its arcs are colored alike. A subdigraph H in D is called rainbow if all its arcs have different colors. A set N ⊆ V (D) is said to be a kernel b...