# 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)

, Volume 28 (4) – Nov 21, 2012
8 pages

/lp/springer-journals/on-the-covering-number-c-3-w-4-3-v-opkDB54cvd
Publisher
Springer Journals
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

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