Clique covers of H-free graphs
It takes <i>n</i><sup>2</sup>/4 cliques to cover all the edges of a complete bipartite graph <i>K</i><sub><i>n/2,n/2</i></sub>, but how many cliques does it take to cover all the edges of a graph <i>G</i> if <i>G</i>...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2023
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| _version_ | 1811139140328095744 |
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| author | Nguyen, T Scott, A Seymour, P Thomassé, S |
| author_facet | Nguyen, T Scott, A Seymour, P Thomassé, S |
| author_sort | Nguyen, T |
| collection | OXFORD |
| description | It takes <i>n</i><sup>2</sup>/4 cliques to cover all the edges of a complete bipartite graph <i>K</i><sub><i>n/2,n/2</i></sub>, but how many cliques does it take to cover all the edges of a graph <i>G</i> if <i>G</i> has no
<i>K</i><sub><i>t,t</i></sub> induced subgraph? We prove that <i>O</i>(<i>n</i><sup><i>2—1/(2t)</i></sup>) cliques suffice for every <i>n</i>-vertex graph; and also prove that, even for graphs with no stable set of size four, we may need more than linearly many cliques. This settles two questions discussed at a recent conference in Lyon. |
| first_indexed | 2024-03-07T08:04:40Z |
| format | Journal article |
| id | oxford-uuid:2446685d-4341-4d57-91d7-a8d7c376455e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:01:21Z |
| publishDate | 2023 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:2446685d-4341-4d57-91d7-a8d7c376455e2024-04-29T10:07:24ZClique covers of H-free graphsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2446685d-4341-4d57-91d7-a8d7c376455eEnglishSymplectic ElementsElsevier2023Nguyen, TScott, ASeymour, PThomassé, SIt takes <i>n</i><sup>2</sup>/4 cliques to cover all the edges of a complete bipartite graph <i>K</i><sub><i>n/2,n/2</i></sub>, but how many cliques does it take to cover all the edges of a graph <i>G</i> if <i>G</i> has no <i>K</i><sub><i>t,t</i></sub> induced subgraph? We prove that <i>O</i>(<i>n</i><sup><i>2—1/(2t)</i></sup>) cliques suffice for every <i>n</i>-vertex graph; and also prove that, even for graphs with no stable set of size four, we may need more than linearly many cliques. This settles two questions discussed at a recent conference in Lyon. |
| spellingShingle | Nguyen, T Scott, A Seymour, P Thomassé, S Clique covers of H-free graphs |
| title | Clique covers of H-free graphs |
| title_full | Clique covers of H-free graphs |
| title_fullStr | Clique covers of H-free graphs |
| title_full_unstemmed | Clique covers of H-free graphs |
| title_short | Clique covers of H-free graphs |
| title_sort | clique covers of h free graphs |
| work_keys_str_mv | AT nguyent cliquecoversofhfreegraphs AT scotta cliquecoversofhfreegraphs AT seymourp cliquecoversofhfreegraphs AT thomasses cliquecoversofhfreegraphs |