Balanced bipartite 4-cycle designs

Hung-Lin Fu

Balanced bipartite 4-cycle designs

Hung-Lin Fu^*

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let (λ₁, λ₂, λ₃)K_v1,v2 denote the graph G with V(G) = V₁ ∪ V₂, V₁ ∩ V₂ = 0, |V₁| =v₁, |V₂| = v₂, and the edges of G are obtained by joining (a) each pair of vertices in V_i, i = 1,2, exactly λ_i times and (b) each pair of vertices from V₁ to V₂ exactly λ₃ times. In this paper, we determine all quintuples (λ₁, λ₂, λ₃; v₁, v₂) such that (λ₁, λ₂, λ₃)K_v1,v2 can be decomposed into 4- cycles.

Original language	English
Pages (from-to)	3-26
Number of pages	24
Journal	Australasian Journal of Combinatorics
Volume	32
State	Published - 1 Dec 2005

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title = "Balanced bipartite 4-cycle designs",

abstract = "Let (λ1, λ2, λ3)Kv1,v2 denote the graph G with V(G) = V1 ∪ V2, V1 ∩ V2 = 0, |V1| =v1, |V2| = v2, and the edges of G are obtained by joining (a) each pair of vertices in Vi, i = 1,2, exactly λi times and (b) each pair of vertices from V1 to V2 exactly λ3 times. In this paper, we determine all quintuples (λ1, λ2, λ3; v1, v2) such that (λ1, λ2, λ3)Kv1,v2 can be decomposed into 4- cycles.",

author = "Hung-Lin Fu",

year = "2005",

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journal = "Australasian Journal of Combinatorics",

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N2 - Let (λ1, λ2, λ3)Kv1,v2 denote the graph G with V(G) = V1 ∪ V2, V1 ∩ V2 = 0, |V1| =v1, |V2| = v2, and the edges of G are obtained by joining (a) each pair of vertices in Vi, i = 1,2, exactly λi times and (b) each pair of vertices from V1 to V2 exactly λ3 times. In this paper, we determine all quintuples (λ1, λ2, λ3; v1, v2) such that (λ1, λ2, λ3)Kv1,v2 can be decomposed into 4- cycles.

AB - Let (λ1, λ2, λ3)Kv1,v2 denote the graph G with V(G) = V1 ∪ V2, V1 ∩ V2 = 0, |V1| =v1, |V2| = v2, and the edges of G are obtained by joining (a) each pair of vertices in Vi, i = 1,2, exactly λi times and (b) each pair of vertices from V1 to V2 exactly λ3 times. In this paper, we determine all quintuples (λ1, λ2, λ3; v1, v2) such that (λ1, λ2, λ3)Kv1,v2 can be decomposed into 4- cycles.

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