Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory
For a partially ordered set(A, ≤), letGA be the simple, undirected graph with vertex set A such that two vertices a ≠ ∈ b A are adjacent if either a ≤ b or b a ≤ . We call GA the partial order graph or comparability graph of A. Furthermore, we say that a graph G is a partial order graph if there exi...
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| مؤلفون آخرون: | |
| التنسيق: | article |
| منشور في: |
2020
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/21411 |
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| _version_ | 1864513440315342848 |
|---|---|
| author | Badawi, Ayman |
| author2 | Rissner, Roswitha |
| author2_role | author |
| author_facet | Badawi, Ayman Rissner, Roswitha |
| author_role | author |
| dc.creator.none.fl_str_mv | Badawi, Ayman Rissner, Roswitha |
| dc.date.none.fl_str_mv | 2020 2021-04-14T07:59:18Z 2021-04-14T07:59:18Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Badawi, A., & Rissner, R. (2020). Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory. Open Mathematics, 18(1), 1645-1657. https://doi.org/10.1515/math-2020-0085 2391-5455 http://hdl.handle.net/11073/21411 10.1515/math-2020-0085 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | De Gruyter |
| dc.relation.none.fl_str_mv | https://doi.org/10.1515/math-2020-0085 |
| dc.subject.none.fl_str_mv | Ramsey number Partial order Partial order graph Inclusion graph |
| dc.title.none.fl_str_mv | Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory |
| dc.type.none.fl_str_mv | Peer-Reviewed Published version info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | For a partially ordered set(A, ≤), letGA be the simple, undirected graph with vertex set A such that two vertices a ≠ ∈ b A are adjacent if either a ≤ b or b a ≤ . We call GA the partial order graph or comparability graph of A. Furthermore, we say that a graph G is a partial order graph if there exists a partially ordered set A such that G = GA. For a class of simple, undirected graphs and n, m ≥ 1, we define the Ramsey number (n m, ) with respect to to be the minimal number of vertices r such that every induced subgraph of an arbitrary graph in consisting of r vertices contains either a complete n-clique Kn or an independent set consisting of m vertices. In this paper, we determine the Ramsey number with respect to some classes of partial order graphs. Furthermore, some implications of Ramsey numbers in ring theory are discussed. |
| format | article |
| id | aus_dd1dbf7c24501dbc4a64396b97e132a7 |
| identifier_str_mv | Badawi, A., & Rissner, R. (2020). Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory. Open Mathematics, 18(1), 1645-1657. https://doi.org/10.1515/math-2020-0085 2391-5455 10.1515/math-2020-0085 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/21411 |
| publishDate | 2020 |
| publisher.none.fl_str_mv | De Gruyter |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theoryBadawi, AymanRissner, RoswithaRamsey numberPartial orderPartial order graphInclusion graphFor a partially ordered set(A, ≤), letGA be the simple, undirected graph with vertex set A such that two vertices a ≠ ∈ b A are adjacent if either a ≤ b or b a ≤ . We call GA the partial order graph or comparability graph of A. Furthermore, we say that a graph G is a partial order graph if there exists a partially ordered set A such that G = GA. For a class of simple, undirected graphs and n, m ≥ 1, we define the Ramsey number (n m, ) with respect to to be the minimal number of vertices r such that every induced subgraph of an arbitrary graph in consisting of r vertices contains either a complete n-clique Kn or an independent set consisting of m vertices. In this paper, we determine the Ramsey number with respect to some classes of partial order graphs. Furthermore, some implications of Ramsey numbers in ring theory are discussed.American University of SharjahAustrian Science Fund (FWF)De Gruyter2021-04-14T07:59:18Z2021-04-14T07:59:18Z2020Peer-ReviewedPublished versioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfBadawi, A., & Rissner, R. (2020). Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory. Open Mathematics, 18(1), 1645-1657. https://doi.org/10.1515/math-2020-00852391-5455http://hdl.handle.net/11073/2141110.1515/math-2020-0085en_UShttps://doi.org/10.1515/math-2020-0085oai:repository.aus.edu:11073/214112024-08-22T12:01:37Z |
| spellingShingle | Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory Badawi, Ayman Ramsey number Partial order Partial order graph Inclusion graph |
| status_str | publishedVersion |
| title | Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory |
| title_full | Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory |
| title_fullStr | Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory |
| title_full_unstemmed | Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory |
| title_short | Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory |
| title_sort | Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory |
| topic | Ramsey number Partial order Partial order graph Inclusion graph |
| url | http://hdl.handle.net/11073/21411 |