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首页> 外文期刊>African Journal of Mathematics and Computer Science Research >One kind of construction on sunflower with two petals*
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One kind of construction on sunflower with two petals*

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A sunflower (or ∆-system) with k petals and a core Y is a collection of sets S1,⋯, Sk such that Si∩Sj=Y for all i≠j; the sets S1Y,⋯, Sk Y, are petals. In this paper, we first give a sufficient condition for the existence of a sunflower with 2 petals. Let F={A,B,C} be a family of subsets of a set { a1,⋯,am , b1,⋯,bn , c1,⋯,cn } with ∑ ?? ? ?=? = ∑ ?? ? ?=? + ∑ ?? ? ?=? and A={a1,⋯,am}, B={ b1,⋯,bn } and C={ c1,⋯,cn } are non-increasing lists of nonnegative integers. Suppose that for each r with ? ≤ ? ≤ ?, ∑ ?? ? ?=? ≤ ∑ ???{??, ?} ? ?=? + ∑ ???{??, ?} ? ?=? , then the family F* contains a sunflower with two petals, where F * ={G1 ,G2}, G1=GY∪X and G2= Z∪X are the subgraphs induced respectively by Y∪X and Z∪X with ??? (??) = ?? for all vj ∈Y∪X and ??? (??) = ?? for all vj∈Z∪X. Moreover, we generalize the consequence to the case of a much more general result.

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