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

On the covering number c λ(3,W 4 (3) , v) A t-hyperwheel (t ≥ 3) of length l (or W l (t) 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 4 (3) , v) is investigated. Direct and recursive constructions on MC λ (3,W 4 (3) , v) are presented. The covering number c λ (3,W 4 (3) , v) is finally determined for any positive integers v ≥ 5 and λ. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

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

Acta Mathematicae Applicatae Sinica , Volume 28 (4) – Nov 21, 2012

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0178-y
Publisher site
See Article on Publisher Site

Abstract

A t-hyperwheel (t ≥ 3) of length l (or W l (t) 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 4 (3) , v) is investigated. Direct and recursive constructions on MC λ (3,W 4 (3) , v) are presented. The covering number c λ (3,W 4 (3) , v) is finally determined for any positive integers v ≥ 5 and λ.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 21, 2012

References