‎Let Γa be a graph whose each vertex is colored either white or black‎. ‎If u is a black vertex of Γ such that exactly one neighbor‎ ‎v of u is white‎, ‎then u changes the color of v to black‎. ‎A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that‎ if initially the vertices in Z are colored black and the remaining vertices are colored white‎, ‎then Z changes the col...

Relative diffuse reflection measurements from the original and ground surfaces using a He-Ne laser are reported. The intensity measurements for the metallic, transparent dielectric, matte plastic surfaces and colored papers are presented. Our results indicate that among metallic surfaces tested, aluminum has the highest diffuse reflectance; while the original stainless steel surface shows the l...

We introduce a colored coalescent process which recovers random colored genealogical trees. Here a colored genealogical tree has its vertices colored black or white. Moving backward along the colored genealogical tree, the color of vertices may change only when two vertice coalesce. The rule that governs the change of color involves a parameter x. When x = 1/2, the colored coalescent process ca...

An edge-colored graph H is properly colored if no two adjacent edges of H have the same color. In 1997, J. Bang-Jensen and G. Gutin conjectured that an edgecolored complete graph G has a properly colored Hamilton path if and only if G has a spanning subgraph consisting of a properly colored path C0 and a (possibly empty) collection of properly colored cycles C1, C2, . . . , Cd such that V (Ci) ...

We show that the 2-edge-colored chromatic number of a class of simple graphs is bounded if and only if the acyclic chromatic number is bounded for this class. Recently, the CSP dichotomy conjecture has been reduced to the case of 2-edge-colored homomorphism and to the case of 2-vertex-colored homomorphism. Both reductions are rather long and follow the reduction to the case of oriented homomorp...

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...

growing demand of invisible braces byesthetically conscious patients has led to remarkable inventions in materials for esthetic labial archwires. archwires with excellent optical clarity and mechanical properties comparable to conventional archwires have been manufactured by almost all the leading companies of orthodontic products in the past two decades, but their clinical use is still limited...

We characterize edge-colored graphs in which every edge belongs to some properly colored cycle. We obtain our result by applying a characterization of 1-extendable graphs.

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