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In this paper we consider optimal edge colored complete graphs. We show that in any optimal edge coloring of the complete graph Kn, there is a Hamilton cycle with at most √ 8n different colors. We also prove that in every proper edge coloring of the complete graph Kn, there is a rainbow cycle with at least n/2−1 colors (A rainbow cycle is a cycle whose all… (More)
In this paper it is shown that every m×n array in which each symbol appears at most (mn− 1)/(m− 1) times has a latin transversal, when n is large enough in comparison to m.
Gibberellic acid (GA3) is a plant hormone belongs to gibberellins. Plants produce low amount of GA3, therefore this hormone is produced by microorganisms. Exogenous GA3 on culture medium was used to increase height of Dyckia maritima shoots to facilitate In vitro manipulation. Grapevine fruits (Thompson seedless) treated with GA3 had increased its size and… (More)
In this paper it is shown that every m× n array in which each symbol appears at most (mn− 1)/(m− 1) times has a transversal, when n 2m3. © 2006 Elsevier B.V. All rights reserved.