Induced subgraphs of graphs with large chromatic number. VI. Banana trees
We investigate which graphs H have the property that in every graph with bounded clique number and sufficiently large chromatic number, some induced subgraph is isomorphic to a subdivision of H. In an earlier paper, the first author proved that every tree has this property; and in another earlier pa...
| Príomhchruthaitheoirí: | , |
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| Formáid: | Journal article |
| Teanga: | English |
| Foilsithe / Cruthaithe: |
Elsevier
2020
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| _version_ | 1826263084525682688 |
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| author | Scott, A Seymour, P |
| author_facet | Scott, A Seymour, P |
| author_sort | Scott, A |
| collection | OXFORD |
| description | We investigate which graphs H have the property that in every graph with bounded clique number and sufficiently large chromatic number, some induced subgraph is isomorphic to a subdivision of H. In an earlier paper, the first author proved that every tree has this property; and in another earlier paper with Maria Chudnovsky, we proved that every cycle has this property. Here we give a common generalization. Say a “banana” is the union of a set of paths all with the same ends but otherwise disjoint. We prove that if H is obtained from a tree by replacing each edge by a banana then H has the property mentioned. |
| first_indexed | 2024-03-06T19:46:05Z |
| format | Journal article |
| id | oxford-uuid:22570a98-ff1c-41f3-8558-5e9bdc756553 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:46:05Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:22570a98-ff1c-41f3-8558-5e9bdc7565532022-03-26T11:38:16ZInduced subgraphs of graphs with large chromatic number. VI. Banana treesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:22570a98-ff1c-41f3-8558-5e9bdc756553EnglishSymplectic ElementsElsevier2020Scott, ASeymour, PWe investigate which graphs H have the property that in every graph with bounded clique number and sufficiently large chromatic number, some induced subgraph is isomorphic to a subdivision of H. In an earlier paper, the first author proved that every tree has this property; and in another earlier paper with Maria Chudnovsky, we proved that every cycle has this property. Here we give a common generalization. Say a “banana” is the union of a set of paths all with the same ends but otherwise disjoint. We prove that if H is obtained from a tree by replacing each edge by a banana then H has the property mentioned. |
| spellingShingle | Scott, A Seymour, P Induced subgraphs of graphs with large chromatic number. VI. Banana trees |
| title | Induced subgraphs of graphs with large chromatic number. VI. Banana trees |
| title_full | Induced subgraphs of graphs with large chromatic number. VI. Banana trees |
| title_fullStr | Induced subgraphs of graphs with large chromatic number. VI. Banana trees |
| title_full_unstemmed | Induced subgraphs of graphs with large chromatic number. VI. Banana trees |
| title_short | Induced subgraphs of graphs with large chromatic number. VI. Banana trees |
| title_sort | induced subgraphs of graphs with large chromatic number vi banana trees |
| work_keys_str_mv | AT scotta inducedsubgraphsofgraphswithlargechromaticnumbervibananatrees AT seymourp inducedsubgraphsofgraphswithlargechromaticnumbervibananatrees |