Minimally non-preperfect graphs of small maximum degree:
Abstract: "A graph G is called preperfect if each induced subgraph G' [subset] G of order at least 2 has two vertices x, y such that either all maximum cliques of G' containing x contain y, or all maximum independent sets of G' containing y contain x, too. Giving a partial answer...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1997
|
| Schriftenreihe: | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin
1997,28 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "A graph G is called preperfect if each induced subgraph G' [subset] G of order at least 2 has two vertices x, y such that either all maximum cliques of G' containing x contain y, or all maximum independent sets of G' containing y contain x, too. Giving a partial answer to a problem of Hammer and Maffray [Combinatorica 13 (1993), 199- 208], we describe new classes of minimally non-preperfect graphs, and prove the following characterizations: (i) A graph of maximum degree 4 is minimally non-preperfect if and only if it is an odd cycle of length at least 5, or the complement of a cycle of length 7, or the line graph of a 3-regular 3-connected bipartite graph. (ii) If a graph G is not an odd cycle and has no isolated vertices, then its line graph is minimally non- perfect if and only if G is bipartite, 3-edge-connected, regular of degree d for some d [> or =] 3, and contains no 3-edge-connected d'-regular subgraph for any 3 [<or =] d' <d." |
| Beschreibung: | 17 S. |
Internformat
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| 100 | 1 | |a Tuza, Zsolt |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Minimally non-preperfect graphs of small maximum degree |c Zsolt Tuza ; Annegret Wagler |
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| 490 | 1 | |a Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin |v 1997,28 | |
| 520 | 3 | |a Abstract: "A graph G is called preperfect if each induced subgraph G' [subset] G of order at least 2 has two vertices x, y such that either all maximum cliques of G' containing x contain y, or all maximum independent sets of G' containing y contain x, too. Giving a partial answer to a problem of Hammer and Maffray [Combinatorica 13 (1993), 199- 208], we describe new classes of minimally non-preperfect graphs, and prove the following characterizations: (i) A graph of maximum degree 4 is minimally non-preperfect if and only if it is an odd cycle of length at least 5, or the complement of a cycle of length 7, or the line graph of a 3-regular 3-connected bipartite graph. (ii) If a graph G is not an odd cycle and has no isolated vertices, then its line graph is minimally non- perfect if and only if G is bipartite, 3-edge-connected, regular of degree d for some d [> or =] 3, and contains no 3-edge-connected d'-regular subgraph for any 3 [<or =] d' <d." | |
| 650 | 4 | |a Graph theory | |
| 650 | 4 | |a Perfect graphs | |
| 700 | 1 | |a Wagler, Annegret |d 1968- |e Verfasser |0 (DE-588)113770227 |4 aut | |
| 810 | 2 | |a Konrad-Zuse-Zentrum für Informationstechnik Berlin |t Preprint SC |v 1997,28 |w (DE-604)BV004801715 |9 1997,28 | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Tuza, Zsolt Wagler, Annegret 1968- |
| author_GND | (DE-588)113770227 |
| author_facet | Tuza, Zsolt Wagler, Annegret 1968- |
| author_role | aut aut |
| author_sort | Tuza, Zsolt |
| author_variant | z t zt a w aw |
| building | Verbundindex |
| bvnumber | BV017189266 |
| classification_rvk | SS 4777 |
| ctrlnum | (OCoLC)38761598 (DE-599)BVBBV017189266 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV017189266 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:14:47Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010360238 |
| oclc_num | 38761598 |
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| owner | DE-703 |
| owner_facet | DE-703 |
| physical | 17 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series2 | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin |
| spelling | Tuza, Zsolt Verfasser aut Minimally non-preperfect graphs of small maximum degree Zsolt Tuza ; Annegret Wagler Berlin Konrad-Zuse-Zentrum für Informationstechnik 1997 17 S. txt rdacontent n rdamedia nc rdacarrier Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin 1997,28 Abstract: "A graph G is called preperfect if each induced subgraph G' [subset] G of order at least 2 has two vertices x, y such that either all maximum cliques of G' containing x contain y, or all maximum independent sets of G' containing y contain x, too. Giving a partial answer to a problem of Hammer and Maffray [Combinatorica 13 (1993), 199- 208], we describe new classes of minimally non-preperfect graphs, and prove the following characterizations: (i) A graph of maximum degree 4 is minimally non-preperfect if and only if it is an odd cycle of length at least 5, or the complement of a cycle of length 7, or the line graph of a 3-regular 3-connected bipartite graph. (ii) If a graph G is not an odd cycle and has no isolated vertices, then its line graph is minimally non- perfect if and only if G is bipartite, 3-edge-connected, regular of degree d for some d [> or =] 3, and contains no 3-edge-connected d'-regular subgraph for any 3 [<or =] d' <d." Graph theory Perfect graphs Wagler, Annegret 1968- Verfasser (DE-588)113770227 aut Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 1997,28 (DE-604)BV004801715 1997,28 |
| spellingShingle | Tuza, Zsolt Wagler, Annegret 1968- Minimally non-preperfect graphs of small maximum degree Graph theory Perfect graphs |
| title | Minimally non-preperfect graphs of small maximum degree |
| title_auth | Minimally non-preperfect graphs of small maximum degree |
| title_exact_search | Minimally non-preperfect graphs of small maximum degree |
| title_full | Minimally non-preperfect graphs of small maximum degree Zsolt Tuza ; Annegret Wagler |
| title_fullStr | Minimally non-preperfect graphs of small maximum degree Zsolt Tuza ; Annegret Wagler |
| title_full_unstemmed | Minimally non-preperfect graphs of small maximum degree Zsolt Tuza ; Annegret Wagler |
| title_short | Minimally non-preperfect graphs of small maximum degree |
| title_sort | minimally non preperfect graphs of small maximum degree |
| topic | Graph theory Perfect graphs |
| topic_facet | Graph theory Perfect graphs |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT tuzazsolt minimallynonpreperfectgraphsofsmallmaximumdegree AT waglerannegret minimallynonpreperfectgraphsofsmallmaximumdegree |