Four‐terminus flows

P. D. Seymour

doi:10.1002/net.3230100108

Four‐terminus flows

P. D. Seymour

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

26 Scopus citations

Abstract

Suppose that s₁, s₂, s₃, s₄ are vertices of a graph, that each edge has a real‐valued capacity, and q_ii(1 ⩽ i < j ⩽ 4) are six demands. There exist flows from s_i to s_j of value q_ij(1 ⩽ i < j ⩽ 4), such that the total flow through each edge does not exceed its capacity, if and only if the obvious connectivity requirements are satisfied. This result extends Hu's 2‐commodity flow theorem.

Original language	English (US)
Pages (from-to)	79-86
Number of pages	8
Journal	Networks
Volume	10
Issue number	1
DOIs	https://doi.org/10.1002/net.3230100108
State	Published - 1980
Externally published	Yes

All Science Journal Classification (ASJC) codes

Software
Information Systems
Hardware and Architecture
Computer Networks and Communications

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10.1002/net.3230100108

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title = "Four‐terminus flows",

abstract = "Suppose that s1, s2, s3, s4 are vertices of a graph, that each edge has a real‐valued capacity, and qii(1 ⩽ i < j ⩽ 4) are six demands. There exist flows from si to sj of value qij(1 ⩽ i < j ⩽ 4), such that the total flow through each edge does not exceed its capacity, if and only if the obvious connectivity requirements are satisfied. This result extends Hu's 2‐commodity flow theorem.",

author = "Seymour, {P. D.}",

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T1 - Four‐terminus flows

AU - Seymour, P. D.

PY - 1980

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N2 - Suppose that s1, s2, s3, s4 are vertices of a graph, that each edge has a real‐valued capacity, and qii(1 ⩽ i < j ⩽ 4) are six demands. There exist flows from si to sj of value qij(1 ⩽ i < j ⩽ 4), such that the total flow through each edge does not exceed its capacity, if and only if the obvious connectivity requirements are satisfied. This result extends Hu's 2‐commodity flow theorem.

AB - Suppose that s1, s2, s3, s4 are vertices of a graph, that each edge has a real‐valued capacity, and qii(1 ⩽ i < j ⩽ 4) are six demands. There exist flows from si to sj of value qij(1 ⩽ i < j ⩽ 4), such that the total flow through each edge does not exceed its capacity, if and only if the obvious connectivity requirements are satisfied. This result extends Hu's 2‐commodity flow theorem.

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DO - 10.1002/net.3230100108

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EP - 86

JO - Networks

JF - Networks

IS - 1

ER -

Four‐terminus flows

Abstract

All Science Journal Classification (ASJC) codes

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