Zero-Sum Flows in Regular Graphs
For an undirected graph G , a zero-sum flow is an assignment of non-zero real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero. It has been conjectured that if a graph G has a zero-sum flow, then it has a zero-sum 6-flow. We prove this conjecture a...
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| Veröffentlicht in: | Graphs and combinatorics 2010-09, Vol.26 (5), p.603-615 |
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| creator | Akbari, S. Daemi, A. Hatami, O. Javanmard, A. Mehrabian, A. |
| description | For an undirected graph
G
, a
zero-sum flow
is an assignment of non-zero real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero. It has been conjectured that if a graph
G
has a zero-sum flow, then it has a zero-sum 6-flow. We prove this conjecture and Bouchet’s Conjecture for bidirected graphs are equivalent. Among other results it is shown that if
G
is an
r
-regular graph (
r
≥ 3), then
G
has a zero-sum 7-flow. Furthermore, if
r
is divisible by 3, then
G
has a zero-sum 5-flow. We also show a graph of order
n
with a zero-sum flow has a zero-sum (
n
+ 3)
2
-flow. Finally, the existence of
k
-flows for small graphs is investigated. |
| doi_str_mv | 10.1007/s00373-010-0946-5 |
| format | Article |
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G
, a
zero-sum flow
is an assignment of non-zero real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero. It has been conjectured that if a graph
G
has a zero-sum flow, then it has a zero-sum 6-flow. We prove this conjecture and Bouchet’s Conjecture for bidirected graphs are equivalent. Among other results it is shown that if
G
is an
r
-regular graph (
r
≥ 3), then
G
has a zero-sum 7-flow. Furthermore, if
r
is divisible by 3, then
G
has a zero-sum 5-flow. We also show a graph of order
n
with a zero-sum flow has a zero-sum (
n
+ 3)
2
-flow. Finally, the existence of
k
-flows for small graphs is investigated.</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-010-0946-5</identifier><language>eng</language><publisher>Japan: Springer Japan</publisher><subject>Combinatorial analysis ; Combinatorics ; Engineering Design ; Equivalence ; Graph theory ; Graphs ; Mathematics ; Mathematics and Statistics ; Original Paper ; Real numbers</subject><ispartof>Graphs and combinatorics, 2010-09, Vol.26 (5), p.603-615</ispartof><rights>Springer 2010</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c347t-eeb09de6c575f0b90a2b401294f07c58959274d664f885792978eeaea57892673</citedby><cites>FETCH-LOGICAL-c347t-eeb09de6c575f0b90a2b401294f07c58959274d664f885792978eeaea57892673</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00373-010-0946-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00373-010-0946-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Akbari, S.</creatorcontrib><creatorcontrib>Daemi, A.</creatorcontrib><creatorcontrib>Hatami, O.</creatorcontrib><creatorcontrib>Javanmard, A.</creatorcontrib><creatorcontrib>Mehrabian, A.</creatorcontrib><title>Zero-Sum Flows in Regular Graphs</title><title>Graphs and combinatorics</title><addtitle>Graphs and Combinatorics</addtitle><description>For an undirected graph
G
, a
zero-sum flow
is an assignment of non-zero real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero. It has been conjectured that if a graph
G
has a zero-sum flow, then it has a zero-sum 6-flow. We prove this conjecture and Bouchet’s Conjecture for bidirected graphs are equivalent. Among other results it is shown that if
G
is an
r
-regular graph (
r
≥ 3), then
G
has a zero-sum 7-flow. Furthermore, if
r
is divisible by 3, then
G
has a zero-sum 5-flow. We also show a graph of order
n
with a zero-sum flow has a zero-sum (
n
+ 3)
2
-flow. Finally, the existence of
k
-flows for small graphs is investigated.</description><subject>Combinatorial analysis</subject><subject>Combinatorics</subject><subject>Engineering Design</subject><subject>Equivalence</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Real numbers</subject><issn>0911-0119</issn><issn>1435-5914</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKs_wNvixVN08rXJHKVoFQqCHxcvId3O1pbtbk26iP_elBUEwdMc5nlfZh7GzgVcCQB7nQCUVRwEcEBdcnPARkIrww0KfchGgELkrcBjdpLSGgCM0DBixRvFjj_3m-Ku6T5TsWqLJ1r2TYjFNIbtezplR3VoEp39zDF7vbt9mdzz2eP0YXIz45XSdseJ5oALKitjTQ1zhCDnGoREXYOtjEOD0upFWeraOWNRonVEgYKxDmVp1ZhdDr3b2H30lHZ-s0oVNU1oqeuTd8I5pTXKTF78IdddH9t8nLcatVMqPz5mYoCq2KUUqfbbuNqE-OUF-L0xPxjz2ZjfG_MmZ-SQSZltlxR_i_8PfQO_j2pF</recordid><startdate>20100901</startdate><enddate>20100901</enddate><creator>Akbari, S.</creator><creator>Daemi, A.</creator><creator>Hatami, O.</creator><creator>Javanmard, A.</creator><creator>Mehrabian, A.</creator><general>Springer Japan</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20100901</creationdate><title>Zero-Sum Flows in Regular Graphs</title><author>Akbari, S. ; Daemi, A. ; Hatami, O. ; Javanmard, A. ; Mehrabian, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c347t-eeb09de6c575f0b90a2b401294f07c58959274d664f885792978eeaea57892673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Combinatorial analysis</topic><topic>Combinatorics</topic><topic>Engineering Design</topic><topic>Equivalence</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Real numbers</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Akbari, S.</creatorcontrib><creatorcontrib>Daemi, A.</creatorcontrib><creatorcontrib>Hatami, O.</creatorcontrib><creatorcontrib>Javanmard, A.</creatorcontrib><creatorcontrib>Mehrabian, A.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Graphs and combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Akbari, S.</au><au>Daemi, A.</au><au>Hatami, O.</au><au>Javanmard, A.</au><au>Mehrabian, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Zero-Sum Flows in Regular Graphs</atitle><jtitle>Graphs and combinatorics</jtitle><stitle>Graphs and Combinatorics</stitle><date>2010-09-01</date><risdate>2010</risdate><volume>26</volume><issue>5</issue><spage>603</spage><epage>615</epage><pages>603-615</pages><issn>0911-0119</issn><eissn>1435-5914</eissn><abstract>For an undirected graph
G
, a
zero-sum flow
is an assignment of non-zero real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero. It has been conjectured that if a graph
G
has a zero-sum flow, then it has a zero-sum 6-flow. We prove this conjecture and Bouchet’s Conjecture for bidirected graphs are equivalent. Among other results it is shown that if
G
is an
r
-regular graph (
r
≥ 3), then
G
has a zero-sum 7-flow. Furthermore, if
r
is divisible by 3, then
G
has a zero-sum 5-flow. We also show a graph of order
n
with a zero-sum flow has a zero-sum (
n
+ 3)
2
-flow. Finally, the existence of
k
-flows for small graphs is investigated.</abstract><cop>Japan</cop><pub>Springer Japan</pub><doi>10.1007/s00373-010-0946-5</doi><tpages>13</tpages></addata></record> |
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| ispartof | Graphs and combinatorics, 2010-09, Vol.26 (5), p.603-615 |
| issn | 0911-0119 1435-5914 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_818834492 |
| source | Springer Online Journals - JUSTICE |
| subjects | Combinatorial analysis Combinatorics Engineering Design Equivalence Graph theory Graphs Mathematics Mathematics and Statistics Original Paper Real numbers |
| title | Zero-Sum Flows in Regular Graphs |
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