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On the covering number c λ(3,W (3)4 , v)

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Abstract

A t-hyperwheel (t ≥ 3) of length l (or W (t) l for brevity) is a t-uniform hypergraph (V,E), where E = {e 1, e 2, …, e l } and v 1, v 2, …, v l are distinct vertices of \(V = \bigcup\limits_{i = 1}^l {e_i } \) such that for i = 1, …, l, v i , v i +1 ∈ e i and e i ∩ e j = P, j ∋ {i − 1, i, i + 1}, where the operation on the subscripts is modulo l and P is a vertex of V which is different from v i , 1 ≤ i ≤ l. In this paper, the minimum covering problem of MC λ (3,W (3)4 , v) is investigated. Direct and recursive constructions on MC λ (3,W (3)4 , v) are presented. The covering number c λ (3,W (3)4 , v) is finally determined for any positive integers v ≥ 5 and λ.

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Authors and Affiliations

  1. Institute of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Yan Wu & Yan-xun Chang

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  1. Yan Wu
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  2. Yan-xun Chang
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Correspondence to Yan-xun Chang.

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Supported by the National Natural Science Foundation of China (No. 10771013 and 10831002).

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Wu, Y., Chang, Yx. On the covering number c λ(3,W (3)4 , v). Acta Math. Appl. Sin. Engl. Ser. 28, 631–638 (2012). https://doi.org/10.1007/s10255-012-0178-y

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  • DOI: https://doi.org/10.1007/s10255-012-0178-y

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