1984: Science's Multicolored Coat

Monochromatic Vs multicolored paths

Let l and k be positive integers, and let X = {0, 1, . . . , l}. Is it true that for every coloring δ : X × X → {0, 1, . . .} there either exist elements x0 < x1 < . . . < xl of X with δ(x0, x1) = δ(x1, x2) = . . . = δ(xl−1, xl), or else there exist elements y0 < y1 < . . . < yk of X with δ(yi−1, yi) 6= δ(yj−1, yj) for all 1 ≤ i < j ≤ k? We prove here that this is the case if either l ≤ 2, or k...

Multicolored vertical silicon nanowires.

We demonstrate that vertical silicon nanowires take on a surprising variety of colors covering the entire visible spectrum, in marked contrast to the gray color of bulk silicon. This effect is readily observable by bright-field microscopy, or even to the naked eye. The reflection spectra of the nanowires each show a dip whose position depends on the nanowire radii. We compare the experimental d...

Multicolored matchings in hypergraphs

For a collection of (not necessarily distinct) matchingsM = (M1,M2, . . . ,Mq) in a hypergraph, where each matching is of size t, a matching M of size t contained in the union ∪i=1Mi is called a rainbow matching if there is an injective mapping from M to M assigning to each edge e of M a matching Mi ∈M containing e. Let f(r, t) denote the maximum k for which there exists a collection of k match...

Multicolored Trees in Random Graphs

Multicolored Dynamos on Toroidal Meshes

Detecting on a graph the presence of the minimum number of nodes (target set) that will be able to “activate” a prescribed number of vertices in the graph is called the target set selection problem (TSS) proposed by Kempe, Kleinberg, and Tardos. In TSS’s settings, nodes have two possible states (active or non-active) and the threshold triggering the activation of a node is given by the number o...