Edge-transitive uniface embeddings of bipartite multi-graphs
It is shown that a bipartite multi-graph Γ has an orientably edge-transitive embedding with a single face if and only if Γ = K m , n ( λ ) such that gcd ( m , n ) = 1 and mn is even whenever λ is even. A consequence of this shows that each orientable surface carries a simple edge-transitive map with...
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| Veröffentlicht in: | Journal of algebraic combinatorics 2019-03, Vol.49 (2), p.125-134 |
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| container_title | Journal of algebraic combinatorics |
| container_volume | 49 |
| creator | Fan, Wenwen Li, Cai Heng Wang, Naer |
| description | It is shown that a bipartite multi-graph
Γ
has an orientably edge-transitive embedding with a single face if and only if
Γ
=
K
m
,
n
(
λ
)
such that
gcd
(
m
,
n
)
=
1
and
mn
is even whenever
λ
is even. A consequence of this shows that each orientable surface carries a simple edge-transitive map with a single face. |
| doi_str_mv | 10.1007/s10801-018-0821-7 |
| format | Article |
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Γ
has an orientably edge-transitive embedding with a single face if and only if
Γ
=
K
m
,
n
(
λ
)
such that
gcd
(
m
,
n
)
=
1
and
mn
is even whenever
λ
is even. A consequence of this shows that each orientable surface carries a simple edge-transitive map with a single face.</description><identifier>ISSN: 0925-9899</identifier><identifier>EISSN: 1572-9192</identifier><identifier>DOI: 10.1007/s10801-018-0821-7</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Alliances ; Combinatorics ; Computer Science ; Convex and Discrete Geometry ; Graph theory ; Group Theory and Generalizations ; Lattices ; Mathematics ; Mathematics and Statistics ; Order ; Ordered Algebraic Structures</subject><ispartof>Journal of algebraic combinatorics, 2019-03, Vol.49 (2), p.125-134</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-f36ea2c0d3e78adf2b9e798838281815bfffc6baa75a817824aaef5d0a7ebf683</citedby><cites>FETCH-LOGICAL-c359t-f36ea2c0d3e78adf2b9e798838281815bfffc6baa75a817824aaef5d0a7ebf683</cites><orcidid>0000-0002-9661-9515</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10801-018-0821-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10801-018-0821-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Fan, Wenwen</creatorcontrib><creatorcontrib>Li, Cai Heng</creatorcontrib><creatorcontrib>Wang, Naer</creatorcontrib><title>Edge-transitive uniface embeddings of bipartite multi-graphs</title><title>Journal of algebraic combinatorics</title><addtitle>J Algebr Comb</addtitle><description>It is shown that a bipartite multi-graph
Γ
has an orientably edge-transitive embedding with a single face if and only if
Γ
=
K
m
,
n
(
λ
)
such that
gcd
(
m
,
n
)
=
1
and
mn
is even whenever
λ
is even. A consequence of this shows that each orientable surface carries a simple edge-transitive map with a single face.</description><subject>Alliances</subject><subject>Combinatorics</subject><subject>Computer Science</subject><subject>Convex and Discrete Geometry</subject><subject>Graph theory</subject><subject>Group Theory and Generalizations</subject><subject>Lattices</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Order</subject><subject>Ordered Algebraic Structures</subject><issn>0925-9899</issn><issn>1572-9192</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLxDAQhYMouK7-AG8Fz9GZ1DYJeJFlXYUFL3oOaTupWXbbmqSC_94uFTx5msv33hs-xq4RbhFA3kUEBcgBFQclkMsTtsBCCq5Ri1O2AC0KrpXW5-wixh0AaIXFgj2sm5Z4CraLPvkvysbOO1tTRoeKmsZ3bcx6l1V-sCH5RNlh3CfP22CHj3jJzpzdR7r6vUv2_rR-Wz3z7evmZfW45XVe6MRdXpIVNTQ5SWUbJypNUiuVK6Fw-qJyztVlZa0srEKpxL215IoGrKTKlSpfspu5dwj950gxmV0_hm6aNAJ1oTWWEiYKZ6oOfYyBnBmCP9jwbRDMUZKZJZlJkjlKMnLKiDkTJ7ZrKfw1_x_6AdZbaks</recordid><startdate>20190315</startdate><enddate>20190315</enddate><creator>Fan, Wenwen</creator><creator>Li, Cai Heng</creator><creator>Wang, Naer</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-9661-9515</orcidid></search><sort><creationdate>20190315</creationdate><title>Edge-transitive uniface embeddings of bipartite multi-graphs</title><author>Fan, Wenwen ; Li, Cai Heng ; Wang, Naer</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-f36ea2c0d3e78adf2b9e798838281815bfffc6baa75a817824aaef5d0a7ebf683</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Alliances</topic><topic>Combinatorics</topic><topic>Computer Science</topic><topic>Convex and Discrete Geometry</topic><topic>Graph theory</topic><topic>Group Theory and Generalizations</topic><topic>Lattices</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Order</topic><topic>Ordered Algebraic Structures</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fan, Wenwen</creatorcontrib><creatorcontrib>Li, Cai Heng</creatorcontrib><creatorcontrib>Wang, Naer</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of algebraic combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fan, Wenwen</au><au>Li, Cai Heng</au><au>Wang, Naer</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Edge-transitive uniface embeddings of bipartite multi-graphs</atitle><jtitle>Journal of algebraic combinatorics</jtitle><stitle>J Algebr Comb</stitle><date>2019-03-15</date><risdate>2019</risdate><volume>49</volume><issue>2</issue><spage>125</spage><epage>134</epage><pages>125-134</pages><issn>0925-9899</issn><eissn>1572-9192</eissn><abstract>It is shown that a bipartite multi-graph
Γ
has an orientably edge-transitive embedding with a single face if and only if
Γ
=
K
m
,
n
(
λ
)
such that
gcd
(
m
,
n
)
=
1
and
mn
is even whenever
λ
is even. A consequence of this shows that each orientable surface carries a simple edge-transitive map with a single face.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10801-018-0821-7</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-9661-9515</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of algebraic combinatorics, 2019-03, Vol.49 (2), p.125-134 |
| issn | 0925-9899 1572-9192 |
| language | eng |
| recordid | cdi_proquest_journals_2195991670 |
| source | SpringerLink Journals |
| subjects | Alliances Combinatorics Computer Science Convex and Discrete Geometry Graph theory Group Theory and Generalizations Lattices Mathematics Mathematics and Statistics Order Ordered Algebraic Structures |
| title | Edge-transitive uniface embeddings of bipartite multi-graphs |
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