Let Kc n denote a complete graph on n vertices whose edges are colored in an arbitrary way. Let ∆mon(Kc n) denote the maximum number of edges of the same color incident with a vertex of Kn. A properly colored cycle (path) in Kc n is a cycle (path) in which adjacent edges have distinct colors. B. Bollobás and P. Erdös (1976) proposed the following conjecture: If ∆mon(Kc n) < b 2 c, then Kc n con...

A combinatorial bijection between k-edge colored trees and colored Prüfer codes for labelled trees is established. This bijection gives a simple combinatorial proof for the number k(n − 2)!(nk−n n−2 ) of k-edge colored trees with n vertices.

Mulches bring several benefits to lettuce cultivation.A study on the lettuce ‘Red Rapids’ has been conducted to determine the influence of the different colored plastic mulch on its growth. The experiment consisted of five color treatments as follows; treatment 1- metallic silver (control), treatment 2- red, treatment 3- orange, treatment 4- yellow and treatment 5-green. Results showed that the...

This paper studies the computational complexity of the Proper interval colored graph problem (picg), when the input graph is a colored caterpillar, parameterized by hair length. In order prove our result we establish a close relationship between the picg and a graph layout problem the Proper colored layout problem (pclp). We show a dichotomy: the picg and the pclp are NP-complete for colored ca...

In this note, we give a parity reversing involution on colored binary trees which leads to a combinatorial interpretation of Formula (1.2). We make a simple variation of the bijection between colored ternary trees and binary trees proposed by Sun [2] and find a correspondence between certain class of binary trees and the set of colored 5-ary trees. The generalization of the parity reversing inv...

objective: to study the in vitro color changes of three dental resin veneering materials when immersed in tea, coffee and tamarind extracts. materials and methods: the color changes of heat polymerized tooth colored acrylic resin (stellondetrey, b, f14, dpi dental products of india ltd, mumbai), auto polymerized tooth colored acrylic resin (dpi, b, qv5, dpi dental products of india ltd, mumbai)...

A (m,n)-colored mixed graph is a graph having arcs of m different colors and edges of n different colors. A graph homomorphism of a (m,n)-colored mixed graph G to a (m,n)colored mixed graph H is a vertex mapping such that if uv is an arc (edge) of color c in G, then f(u)f(v) is also an arc (edge) of color c. The (m,n)-colored mixed chromatic number χ(m,n)(G) of a (m,n)-colored mixed graph G, in...

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