Orthogonal (g, f)-factorizations in networks

Peter Che Bor Lam; Guizhen Liu; Guojun Li; Wai Chee Shiu

doi:10.1002/1097-0037(200007)35:4<274::AID-NET6>3.0.CO;2-6

Orthogonal (g, f)-factorizations in networks

Peter Che Bor Lam^*, Guizhen Liu, Guojun Li, Wai Chee Shiu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

29 Citations (Scopus)

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Abstract

Let G = (V, E) be a graph and let g and f be two integer-valued functions defined on V such that k ≤ g(x) ≤ f(x) for all x ∈ V. Let H₁, H₂,⋯, H_k be subgraphs of G such that \E(H_i)\ = m, 1 ≤ i ≤ k, and V(H_i) ∩ V(W_j) = ø when i ≠ j. In this paper, it is proved that every (mg + m - 1, mf - m + 1)-graph G has a (g, f)-factorization orthogonal to H_i for i = 1, 2, ⋯, k and shown that there are polynomial-time algorithms to find the desired (g, f)-factorizations.

Original language	English
Pages (from-to)	274-278
Number of pages	5
Journal	Networks
Volume	35
Issue number	4
Early online date	5 Jun 2000
DOIs	https://doi.org/10.1002/1097-0037(200007)35:4<274::AID-NET6>3.0.CO;2-6
Publication status	Published - Jul 2000

Scopus Subject Areas

Software
Information Systems
Hardware and Architecture
Computer Networks and Communications

User-Defined Keywords

network
graph
(g
f)-factorization
orthogonal factorization

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10.1002/1097-0037(200007)35:4<274::AID-NET6>3.0.CO;2-6

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Cite this

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title = "Orthogonal (g, f)-factorizations in networks",

abstract = "Let G = (V, E) be a graph and let g and f be two integer-valued functions defined on V such that k ≤ g(x) ≤ f(x) for all x ∈ V. Let H1, H2,⋯, Hk be subgraphs of G such that \E(Hi)\ = m, 1 ≤ i ≤ k, and V(Hi) ∩ V(Wj) = {\o} when i ≠ j. In this paper, it is proved that every (mg + m - 1, mf - m + 1)-graph G has a (g, f)-factorization orthogonal to Hi for i = 1, 2, ⋯, k and shown that there are polynomial-time algorithms to find the desired (g, f)-factorizations.",

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AU - Liu, Guizhen

AU - Li, Guojun

AU - Shiu, Wai Chee

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N2 - Let G = (V, E) be a graph and let g and f be two integer-valued functions defined on V such that k ≤ g(x) ≤ f(x) for all x ∈ V. Let H1, H2,⋯, Hk be subgraphs of G such that \E(Hi)\ = m, 1 ≤ i ≤ k, and V(Hi) ∩ V(Wj) = ø when i ≠ j. In this paper, it is proved that every (mg + m - 1, mf - m + 1)-graph G has a (g, f)-factorization orthogonal to Hi for i = 1, 2, ⋯, k and shown that there are polynomial-time algorithms to find the desired (g, f)-factorizations.

AB - Let G = (V, E) be a graph and let g and f be two integer-valued functions defined on V such that k ≤ g(x) ≤ f(x) for all x ∈ V. Let H1, H2,⋯, Hk be subgraphs of G such that \E(Hi)\ = m, 1 ≤ i ≤ k, and V(Hi) ∩ V(Wj) = ø when i ≠ j. In this paper, it is proved that every (mg + m - 1, mf - m + 1)-graph G has a (g, f)-factorization orthogonal to Hi for i = 1, 2, ⋯, k and shown that there are polynomial-time algorithms to find the desired (g, f)-factorizations.

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KW - graph

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Orthogonal (g, f)-factorizations in networks

Abstract

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