The visualization literature tells us that rainbow color maps are bad, yet domain experts continue to use them. Why? The truth is, we don’t know. It turns out that there is a lot we don’t know about rainbow color maps. Two of the primary reasons our community argues that rainbow color maps are ineffective can be traced back to the idea that rainbow color maps implicitly discretize the encoded d...

A subgraph of an edge-coloured complete graph is called rainbow if all its edges have different colours. In 1980 Hahn conjectured that every properly edge-coloured complete graph Kn has a rainbow Hamiltonian path. Although this conjecture turned out to be false, it was widely believed that such a colouring always contains a rainbow cycle of length almost n. In this paper, improving on several e...

Abstract. Let G be a nontrivial connected graph on which is defined a coloring N k k G E c ∈ → }, ,...., 3 , 2 , 1 { ) ( : , of the edges of G, where adjacent edges may be colored the same. A path in G is called a rainbow path if no two edges of it are colored the same. G is rainbow connected if G contains a rainbow v u − path for every two vertices u and v in it. The minimum k for which there ...

Let HPn,m,k be drawn uniformly from all m-edge, k-uniform, k-partite hypergraphs where each part of the partition is a disjoint copy of [n]. We let HP (κ) n,m,k be an edge colored version, where we color each edge randomly from one of κ colors. We show that if κ = n and m = Kn log n where K is sufficiently large then w.h.p. there is a rainbow colored perfect matching. I.e. a perfect matching in...

Rainbows are a natural cue for calibrating outdoor imagery. While ephemeral, they provide unique calibration cues because they are centered exactly opposite the sun and have an outer radius of 42 degrees. In this work, we define the geometry of a rainbow and describe minimal sets of constraints that are sufficient for estimating camera calibration. We present both semi-automatic and fully autom...

Let G be a graph of order n with an edge coloring c, and let δ(G) denote the minimum color degree of G, i.e., the largest integer such that each vertex of G is incident with at least δ(G) edges having pairwise distinct colors. A subgraph F ⊂ G is rainbow if all edges of F have pairwise distinct colors. In this paper, we prove that (i) if G is triangle-free and δ(G) > n3 + 1, then G contains a r...

Given a collection of matchings M = (M1,M2, . . . ,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be s-rainbow for M if it contains representatives from s matchings Mi (where each edge is allowed to represent just one Mi). Formally, this means that there is a function φ : M → [q] such that e ∈ Mφ(e) for all e ∈ M , and |Im(φ)| > s. Let f(r, s, t) be the maximal k for which ...

We present recent results regarding rainbow matchings in bipartite graphs. Using topological methods we address a known conjecture of Stein and show that if Kn,n is partitioned into n sets of size n, then a partial rainbow matching of size 2n/3 exists. We generalize a result of Cameron and Wanless and show that for any n matchings of size n in a bipartite graph with 2n vertices there exists a f...

background: there are different activating salt solutions for sperm induction of rainbow trout (oncorhynchus mykiss) under artificial spawning condition, although some uncertainties are associated with the performance. objectives: this study was conducted to consider the effects of different concentration of calcium and magnesium ions and change of ph in the billard salt solution on sperm motil...