Graphs of Prescribed Girth and Bi-Degree
We say that a bipartite graph Γ( V 1 ∪ V 2, E) has bi-degree r, s if every vertex from V 1 has degree r and every vertex from V 2 has degree s. Γ is called an ( r, s, t)-graph if, additionally, the girth of Γ is 2 t. For t > 3, very few examples of ( r, s, t)-graphs were previously known. In this...
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| Veröffentlicht in: | Journal of combinatorial theory. Series B 1995-07, Vol.64 (2), p.228-239 |
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| container_title | Journal of combinatorial theory. Series B |
| container_volume | 64 |
| creator | Furedi, Z. Lazebnik, F. Seress, A. Ustimenko, V.A. Woldar, A.J. |
| description | We say that a bipartite graph
Γ(
V
1 ∪
V
2,
E) has bi-degree
r,
s if every vertex from
V
1 has degree
r and every vertex from
V
2 has degree
s.
Γ is called an (
r,
s,
t)-graph if, additionally, the girth of
Γ is 2
t. For
t > 3, very few examples of (
r,
s,
t)-graphs were previously known. In this paper we give a recursive construction of (
r,
s,
t)-graphs for all
r,
s,
t ≥ 2, as well as an algebraic construction of such graphs for all
r,
s ≥
t ≥ 3. |
| doi_str_mv | 10.1006/jctb.1995.1033 |
| format | Article |
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Γ(
V
1 ∪
V
2,
E) has bi-degree
r,
s if every vertex from
V
1 has degree
r and every vertex from
V
2 has degree
s.
Γ is called an (
r,
s,
t)-graph if, additionally, the girth of
Γ is 2
t. For
t > 3, very few examples of (
r,
s,
t)-graphs were previously known. In this paper we give a recursive construction of (
r,
s,
t)-graphs for all
r,
s,
t ≥ 2, as well as an algebraic construction of such graphs for all
r,
s ≥
t ≥ 3.</description><identifier>ISSN: 0095-8956</identifier><identifier>EISSN: 1096-0902</identifier><identifier>DOI: 10.1006/jctb.1995.1033</identifier><language>eng</language><publisher>Elsevier Inc</publisher><ispartof>Journal of combinatorial theory. Series B, 1995-07, Vol.64 (2), p.228-239</ispartof><rights>1995 Academic Press</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c326t-72843981b51e1e78a3b5e5bad7c11eb4fa5fafaf31490381f5d7c977befd08c83</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1006/jctb.1995.1033$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids></links><search><creatorcontrib>Furedi, Z.</creatorcontrib><creatorcontrib>Lazebnik, F.</creatorcontrib><creatorcontrib>Seress, A.</creatorcontrib><creatorcontrib>Ustimenko, V.A.</creatorcontrib><creatorcontrib>Woldar, A.J.</creatorcontrib><title>Graphs of Prescribed Girth and Bi-Degree</title><title>Journal of combinatorial theory. Series B</title><description>We say that a bipartite graph
Γ(
V
1 ∪
V
2,
E) has bi-degree
r,
s if every vertex from
V
1 has degree
r and every vertex from
V
2 has degree
s.
Γ is called an (
r,
s,
t)-graph if, additionally, the girth of
Γ is 2
t. For
t > 3, very few examples of (
r,
s,
t)-graphs were previously known. In this paper we give a recursive construction of (
r,
s,
t)-graphs for all
r,
s,
t ≥ 2, as well as an algebraic construction of such graphs for all
r,
s ≥
t ≥ 3.</description><issn>0095-8956</issn><issn>1096-0902</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1995</creationdate><recordtype>article</recordtype><recordid>eNp1jz1PwzAQhi0EEqGwMmdkcTnHcWyPUGhAqgQDzJY_ztQVNJUdIfHvSVRWdMPp9N5zuoeQawZLBtDd7vzolkxrMY2cn5CKge4oaGhOSQWgBVVadOfkopQdwLQiVUVu-mwP21IPsX7NWHxODkPdpzxua7sP9X2iD_iRES_JWbSfBa_--oK8rx_fVk9089I_r-421POmG6lsVMu1Yk4wZCiV5U6gcDZIzxi6NloR7VSctRq4YlFMiZbSYQygvOILsjze9XkoJWM0h5y-bP4xDMzsaWZPM3ua2XMC1BHA6avvhNkUn3DvMaSMfjRhSP-hv_tiWHc</recordid><startdate>19950701</startdate><enddate>19950701</enddate><creator>Furedi, Z.</creator><creator>Lazebnik, F.</creator><creator>Seress, A.</creator><creator>Ustimenko, V.A.</creator><creator>Woldar, A.J.</creator><general>Elsevier Inc</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19950701</creationdate><title>Graphs of Prescribed Girth and Bi-Degree</title><author>Furedi, Z. ; Lazebnik, F. ; Seress, A. ; Ustimenko, V.A. ; Woldar, A.J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c326t-72843981b51e1e78a3b5e5bad7c11eb4fa5fafaf31490381f5d7c977befd08c83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1995</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Furedi, Z.</creatorcontrib><creatorcontrib>Lazebnik, F.</creatorcontrib><creatorcontrib>Seress, A.</creatorcontrib><creatorcontrib>Ustimenko, V.A.</creatorcontrib><creatorcontrib>Woldar, A.J.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><jtitle>Journal of combinatorial theory. Series B</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Furedi, Z.</au><au>Lazebnik, F.</au><au>Seress, A.</au><au>Ustimenko, V.A.</au><au>Woldar, A.J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Graphs of Prescribed Girth and Bi-Degree</atitle><jtitle>Journal of combinatorial theory. Series B</jtitle><date>1995-07-01</date><risdate>1995</risdate><volume>64</volume><issue>2</issue><spage>228</spage><epage>239</epage><pages>228-239</pages><issn>0095-8956</issn><eissn>1096-0902</eissn><abstract>We say that a bipartite graph
Γ(
V
1 ∪
V
2,
E) has bi-degree
r,
s if every vertex from
V
1 has degree
r and every vertex from
V
2 has degree
s.
Γ is called an (
r,
s,
t)-graph if, additionally, the girth of
Γ is 2
t. For
t > 3, very few examples of (
r,
s,
t)-graphs were previously known. In this paper we give a recursive construction of (
r,
s,
t)-graphs for all
r,
s,
t ≥ 2, as well as an algebraic construction of such graphs for all
r,
s ≥
t ≥ 3.</abstract><pub>Elsevier Inc</pub><doi>10.1006/jctb.1995.1033</doi><tpages>12</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of combinatorial theory. Series B, 1995-07, Vol.64 (2), p.228-239 |
| issn | 0095-8956 1096-0902 |
| language | eng |
| recordid | cdi_crossref_primary_10_1006_jctb_1995_1033 |
| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| title | Graphs of Prescribed Girth and Bi-Degree |
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