Signed graphs: from modulo flows to integer-valued flows Article Swipe

PDF

Jian Cheng , You Lu , Rong Luo , Cun‐Quan Zhang ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1704.08739

Converting modulo flows into integer-valued flows is one of the most critical steps in the study of integer flows. Tutte and Jaeger's pioneering work shows the equivalence of modulo flows and integer-valued flows for ordinary graphs. However, such equivalence does not hold any more for signed graphs. This motivates us to study how to convert modulo flows into integer-valued flows for signed graphs. In this paper, we generalize some early results by Xu and Zhang (Discrete Math.~299, 2005), Schubert and Steffen (European J. Combin.~48, 2015), and Zhu (J. Combin. Theory Ser. B~112, 2015), and show that, for signed graphs, every modulo $(2+\frac{1}{p})$-flow with $p \in {\mathbb Z}^+ \cup \{\infty\}$ can be converted/extended into an integer-valued flow.

Related Topics

Concepts

Modulo Integer (computer science) Mathematics Combinatorics Equivalence (formal languages) Flow (mathematics) Discrete mathematics Geometry Computer science Programming language

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/1704.08739
PDF: https://arxiv.org/pdf/1704.08739
OA Status: green
References: 6
Related Works: 10
OpenAlex ID: https://openalex.org/W2611039006

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W2611039006

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.1704.08739

Digital Object Identifier
Title: Signed graphs: from modulo flows to integer-valued flows

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2017

Year of publication
Publication date: 2017-04-27

Full publication date if available
Authors: Jian Cheng, You Lu, Rong Luo, Cun‐Quan Zhang

List of authors in order
Landing page: https://arxiv.org/abs/1704.08739

Publisher landing page
PDF URL: https://arxiv.org/pdf/1704.08739

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/1704.08739

Direct OA link when available
Concepts: Modulo, Integer (computer science), Mathematics, Combinatorics, Equivalence (formal languages), Flow (mathematics), Discrete mathematics, Geometry, Computer science, Programming language

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
References (count): 6

Number of works referenced by this work
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W2611039006
doi	https://doi.org/10.48550/arxiv.1704.08739
ids.doi	https://doi.org/10.48550/arxiv.1704.08739
ids.mag	2611039006
ids.openalex	https://openalex.org/W2611039006
fwci
type	preprint
title	Signed graphs: from modulo flows to integer-valued flows
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T10374
topics[0].field.id	https://openalex.org/fields/17
topics[0].field.display_name	Computer Science
topics[0].score	0.9962999820709229
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/1703
topics[0].subfield.display_name	Computational Theory and Mathematics
topics[0].display_name	Advanced Graph Theory Research
topics[1].id	https://openalex.org/T11329
topics[1].field.id	https://openalex.org/fields/26
topics[1].field.display_name	Mathematics
topics[1].score	0.9940999746322632
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2607
topics[1].subfield.display_name	Discrete Mathematics and Combinatorics
topics[1].display_name	Limits and Structures in Graph Theory
topics[2].id	https://openalex.org/T12541
topics[2].field.id	https://openalex.org/fields/17
topics[2].field.display_name	Computer Science
topics[2].score	0.9735999703407288
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/1703
topics[2].subfield.display_name	Computational Theory and Mathematics
topics[2].display_name	Graph Labeling and Dimension Problems
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C54732982
concepts[0].level	2
concepts[0].score	0.9106364250183105
concepts[0].wikidata	https://www.wikidata.org/wiki/Q1415345
concepts[0].display_name	Modulo
concepts[1].id	https://openalex.org/C97137487
concepts[1].level	2
concepts[1].score	0.7195470333099365
concepts[1].wikidata	https://www.wikidata.org/wiki/Q729138
concepts[1].display_name	Integer (computer science)
concepts[2].id	https://openalex.org/C33923547
concepts[2].level	0
concepts[2].score	0.708299458026886
concepts[2].wikidata	https://www.wikidata.org/wiki/Q395
concepts[2].display_name	Mathematics
concepts[3].id	https://openalex.org/C114614502
concepts[3].level	1
concepts[3].score	0.6324595212936401
concepts[3].wikidata	https://www.wikidata.org/wiki/Q76592
concepts[3].display_name	Combinatorics
concepts[4].id	https://openalex.org/C2780069185
concepts[4].level	2
concepts[4].score	0.4998135566711426
concepts[4].wikidata	https://www.wikidata.org/wiki/Q7977945
concepts[4].display_name	Equivalence (formal languages)
concepts[5].id	https://openalex.org/C38349280
concepts[5].level	2
concepts[5].score	0.47853073477745056
concepts[5].wikidata	https://www.wikidata.org/wiki/Q1434290
concepts[5].display_name	Flow (mathematics)
concepts[6].id	https://openalex.org/C118615104
concepts[6].level	1
concepts[6].score	0.45150458812713623
concepts[6].wikidata	https://www.wikidata.org/wiki/Q121416
concepts[6].display_name	Discrete mathematics
concepts[7].id	https://openalex.org/C2524010
concepts[7].level	1
concepts[7].score	0.09540441632270813
concepts[7].wikidata	https://www.wikidata.org/wiki/Q8087
concepts[7].display_name	Geometry
concepts[8].id	https://openalex.org/C41008148
concepts[8].level	0
concepts[8].score	0.09308880567550659
concepts[8].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[8].display_name	Computer science
concepts[9].id	https://openalex.org/C199360897
concepts[9].level	1
concepts[9].score	0.0
concepts[9].wikidata	https://www.wikidata.org/wiki/Q9143
concepts[9].display_name	Programming language
keywords[0].id	https://openalex.org/keywords/modulo
keywords[0].score	0.9106364250183105
keywords[0].display_name	Modulo
keywords[1].id	https://openalex.org/keywords/integer
keywords[1].score	0.7195470333099365
keywords[1].display_name	Integer (computer science)
keywords[2].id	https://openalex.org/keywords/mathematics
keywords[2].score	0.708299458026886
keywords[2].display_name	Mathematics
keywords[3].id	https://openalex.org/keywords/combinatorics
keywords[3].score	0.6324595212936401
keywords[3].display_name	Combinatorics
keywords[4].id	https://openalex.org/keywords/equivalence
keywords[4].score	0.4998135566711426
keywords[4].display_name	Equivalence (formal languages)
keywords[5].id	https://openalex.org/keywords/flow
keywords[5].score	0.47853073477745056
keywords[5].display_name	Flow (mathematics)
keywords[6].id	https://openalex.org/keywords/discrete-mathematics
keywords[6].score	0.45150458812713623
keywords[6].display_name	Discrete mathematics
keywords[7].id	https://openalex.org/keywords/geometry
keywords[7].score	0.09540441632270813
keywords[7].display_name	Geometry
keywords[8].id	https://openalex.org/keywords/computer-science
keywords[8].score	0.09308880567550659
keywords[8].display_name	Computer science
language	en
locations[0].id	pmh:oai:arXiv.org:1704.08739
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url	https://arxiv.org/pdf/1704.08739
locations[0].version	submittedVersion
locations[0].raw_type
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/1704.08739
locations[1].id	doi:10.48550/arxiv.1704.08739
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.1704.08739
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5113834335
authorships[0].author.orcid
authorships[0].author.display_name	Jian Cheng
authorships[0].author_position	first
authorships[0].raw_author_name	Jian Cheng
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5004663151
authorships[1].author.orcid	https://orcid.org/0000-0002-7693-9175
authorships[1].author.display_name	You Lu
authorships[1].author_position	middle
authorships[1].raw_author_name	You Lu
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5066405314
authorships[2].author.orcid	https://orcid.org/0000-0002-5237-1001
authorships[2].author.display_name	Rong Luo
authorships[2].author_position	middle
authorships[2].raw_author_name	Rong Luo
authorships[2].is_corresponding	False
authorships[3].author.id	https://openalex.org/A5064703404
authorships[3].author.orcid	https://orcid.org/0000-0001-5583-4481
authorships[3].author.display_name	Cun‐Quan Zhang
authorships[3].author_position	last
authorships[3].raw_author_name	Cun-Quan Zhang
authorships[3].is_corresponding	False
has_content.pdf	True
has_content.grobid_xml	True
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/1704.08739
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Signed graphs: from modulo flows to integer-valued flows
has_fulltext	True
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T10374
primary_topic.field.id	https://openalex.org/fields/17
primary_topic.field.display_name	Computer Science
primary_topic.score	0.9962999820709229
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/1703
primary_topic.subfield.display_name	Computational Theory and Mathematics
primary_topic.display_name	Advanced Graph Theory Research
related_works	https://openalex.org/W4391375266, https://openalex.org/W2117548279, https://openalex.org/W2097470475, https://openalex.org/W2070252991, https://openalex.org/W2807449856, https://openalex.org/W2941201715, https://openalex.org/W2025727968, https://openalex.org/W238211858, https://openalex.org/W4297742300, https://openalex.org/W4394650166
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:1704.08739
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url	https://arxiv.org/pdf/1704.08739
best_oa_location.version	submittedVersion
best_oa_location.raw_type
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/1704.08739
primary_location.id	pmh:oai:arXiv.org:1704.08739
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url	https://arxiv.org/pdf/1704.08739
primary_location.version	submittedVersion
primary_location.raw_type
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/1704.08739
publication_date	2017-04-27
publication_year	2017
referenced_works	https://openalex.org/W2068987903, https://openalex.org/W1584148193, https://openalex.org/W2087348204, https://openalex.org/W2095645574, https://openalex.org/W1786780942, https://openalex.org/W2011470163
referenced_works_count	6
abstract_inverted_index.$p	103
abstract_inverted_index.In	63
abstract_inverted_index.J.	82
abstract_inverted_index.Xu	72
abstract_inverted_index.an	113
abstract_inverted_index.be	110
abstract_inverted_index.by	71
abstract_inverted_index.in	13
abstract_inverted_index.is	6
abstract_inverted_index.of	8, 16, 27
abstract_inverted_index.to	50, 53
abstract_inverted_index.us	49
abstract_inverted_index.we	66
abstract_inverted_index.(J.	87
abstract_inverted_index.Zhu	86
abstract_inverted_index.\in	104
abstract_inverted_index.and	20, 30, 73, 79, 85, 93
abstract_inverted_index.any	42
abstract_inverted_index.can	109
abstract_inverted_index.for	33, 44, 60, 96
abstract_inverted_index.how	52
abstract_inverted_index.not	40
abstract_inverted_index.one	7
abstract_inverted_index.the	9, 14, 25
abstract_inverted_index.Ser.	90
abstract_inverted_index.This	47
abstract_inverted_index.Z}^+	106
abstract_inverted_index.\cup	107
abstract_inverted_index.does	39
abstract_inverted_index.hold	41
abstract_inverted_index.into	3, 57, 112
abstract_inverted_index.more	43
abstract_inverted_index.most	10
abstract_inverted_index.show	94
abstract_inverted_index.some	68
abstract_inverted_index.such	37
abstract_inverted_index.this	64
abstract_inverted_index.with	102
abstract_inverted_index.work	23
abstract_inverted_index.Tutte	19
abstract_inverted_index.Zhang	74
abstract_inverted_index.early	69
abstract_inverted_index.every	99
abstract_inverted_index.flow.	115
abstract_inverted_index.flows	2, 5, 29, 32, 56, 59
abstract_inverted_index.shows	24
abstract_inverted_index.steps	12
abstract_inverted_index.study	15, 51
abstract_inverted_index.that,	95
abstract_inverted_index.2005),	77
abstract_inverted_index.2015),	84, 92
abstract_inverted_index.B~112,	91
abstract_inverted_index.Theory	89
abstract_inverted_index.flows.	18
abstract_inverted_index.modulo	1, 28, 55, 100
abstract_inverted_index.paper,	65
abstract_inverted_index.signed	45, 61, 97
abstract_inverted_index.Combin.	88
abstract_inverted_index.Steffen	80
abstract_inverted_index.convert	54
abstract_inverted_index.graphs,	98
abstract_inverted_index.graphs.	35, 46, 62
abstract_inverted_index.integer	17
abstract_inverted_index.results	70
abstract_inverted_index.However,	36
abstract_inverted_index.Jaeger's	21
abstract_inverted_index.Schubert	78
abstract_inverted_index.critical	11
abstract_inverted_index.ordinary	34
abstract_inverted_index.{\mathbb	105
abstract_inverted_index.(Discrete	75
abstract_inverted_index.(European	81
abstract_inverted_index.motivates	48
abstract_inverted_index.Converting	0
abstract_inverted_index.Math.~299,	76
abstract_inverted_index.generalize	67
abstract_inverted_index.pioneering	22
abstract_inverted_index.Combin.~48,	83
abstract_inverted_index.\{\infty\}$	108
abstract_inverted_index.equivalence	26, 38
abstract_inverted_index.integer-valued	4, 31, 58, 114
abstract_inverted_index.converted/extended	111
abstract_inverted_index.$(2+\frac{1}{p})$-flow	101
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	4
citation_normalized_percentile