In 2009, Blagojević, Matschke & Ziegler established the first tight colored Tverberg theorem. We develop a colored version of our previous results (2008): Evenness and non-trivial lower bounds for the number of colored Tverberg partitions. Both properties follow from similar results on the number of colored Birch partitions.

Let S be a set of n points in general position on the plane. For a given point p not in S, a radial ordering of S with respect to p is a circular ordering of the elements of S by angle around p. If S is bi-colored, with equal sized color classes, then a colored radial ordering of S with respect to p is a circular ordering by angle of the colors of the points of S around p, that is, permutations...

O R IG IN A L A R T IC L E Ursula Rohr Sgarbieri

The structure of edge-colored complete graphs containing no properly colored triangles has been characterized by Gallai back in the 1960s. More recently, Cǎda et al. and Fujita independently determined bipartite C 4 . We characterize even cycles, or equivalently, without a 6 In particular, we first deal with simple case 2-edge-colored graphs, using result Yeo. Next, for k ≥ 3, define four class...

O R IG IN A L A R T IC L E Alexandre Rodrigues Guerzoni Érika Cristina Pavarino-Bertelli Moacir Fernandes de Godoy

Colored range queries are a well-studied topic in computational geometry and database research that, in the past decade, have found exciting applications in information retrieval. In this paper we give improved time and space bounds for three important one-dimensional colored range queries — colored range listing, colored range top-k queries and colored range counting — and, thus, new bounds fo...

Traditionally, stochastic differential equations used in the physical sciences have involved Gaussian white noise. ' In recent times, however, white noise has been replaced by colored noise in a variety of contexts. Laser noise problems and first passage time problems have been shown to necessitate the use of colored noise instead of white noise. Even the mathematical foundations for the theory...

We first consider the following problem. We are given a fixed perfect matching M of [n] and we add random edges one at a time until there is a Hamilton cycle containing M . We show that w.h.p. the hitting time for this event is the same as that for the first time there are no isolated vertices in the graph induced by the random edges. We then use this result for the following problem. We genera...

It is shown that for every > 0 and n > n0( ), any complete graph K on n vertices whose edges are colored so that no vertex is incident with more than (1 − 1 √ 2 − )n edges of the same color, contains a Hamilton cycle in which adjacent edges have distinct colors. Moreover, for every k between 3 and n any such K contains a cycle of length k in which adjacent edges have distinct colors.