Finding a Strong Stable Set or a Meyniel Obstruction in any Graph
A strong stable set in a graph $G$ is a stable set that contains a vertex of every maximal clique of $G$. A Meyniel obstruction is an odd circuit with at least five vertices and at most one chord. Given a graph $G$ and a vertex $v$ of $G$, we give a polytime algorithm to find either a strong stable...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2005-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/3411/pdf |
| _version_ | 1797270343117701120 |
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| author | Kathie Cameron Jack Edmonds |
| author_facet | Kathie Cameron Jack Edmonds |
| author_sort | Kathie Cameron |
| collection | DOAJ |
| description | A strong stable set in a graph $G$ is a stable set that contains a vertex of every maximal clique of $G$. A Meyniel obstruction is an odd circuit with at least five vertices and at most one chord. Given a graph $G$ and a vertex $v$ of $G$, we give a polytime algorithm to find either a strong stable set containing $v$ or a Meyniel obstruction in $G$. This can then be used to find in any graph, a clique and colouring of the same size or a Meyniel obstruction. |
| first_indexed | 2024-04-25T02:02:45Z |
| format | Article |
| id | doaj.art-4194543b86fc4da7b56dddcea6616679 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:45Z |
| publishDate | 2005-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-4194543b86fc4da7b56dddcea66166792024-03-07T14:41:15ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502005-01-01DMTCS Proceedings vol. AE,...Proceedings10.46298/dmtcs.34113411Finding a Strong Stable Set or a Meyniel Obstruction in any GraphKathie Cameron0Jack Edmonds1Department of Mathematics, Wilfrid Laurier UniversityDepartment of Mathematics, Wilfrid Laurier UniversityA strong stable set in a graph $G$ is a stable set that contains a vertex of every maximal clique of $G$. A Meyniel obstruction is an odd circuit with at least five vertices and at most one chord. Given a graph $G$ and a vertex $v$ of $G$, we give a polytime algorithm to find either a strong stable set containing $v$ or a Meyniel obstruction in $G$. This can then be used to find in any graph, a clique and colouring of the same size or a Meyniel obstruction.https://dmtcs.episciences.org/3411/pdfstable setindependent setgraph colouringmeyniel graphperfect graph[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Kathie Cameron Jack Edmonds Finding a Strong Stable Set or a Meyniel Obstruction in any Graph Discrete Mathematics & Theoretical Computer Science stable set independent set graph colouring meyniel graph perfect graph [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | Finding a Strong Stable Set or a Meyniel Obstruction in any Graph |
| title_full | Finding a Strong Stable Set or a Meyniel Obstruction in any Graph |
| title_fullStr | Finding a Strong Stable Set or a Meyniel Obstruction in any Graph |
| title_full_unstemmed | Finding a Strong Stable Set or a Meyniel Obstruction in any Graph |
| title_short | Finding a Strong Stable Set or a Meyniel Obstruction in any Graph |
| title_sort | finding a strong stable set or a meyniel obstruction in any graph |
| topic | stable set independent set graph colouring meyniel graph perfect graph [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/3411/pdf |
| work_keys_str_mv | AT kathiecameron findingastrongstablesetorameynielobstructioninanygraph AT jackedmonds findingastrongstablesetorameynielobstructioninanygraph |