On the critical densities of minor-closed classes
Given a minor-closed class A of graphs, let βAdenote the supremum over all graphs in A of the ratio of edges to vertices. We investigate the set B of all such values βA, taking further the project begun by Eppstein. Amongst other results, we determine the small values in B (those up to 2); we show t...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Published: |
Elsevier
2018
|
| _version_ | 1826257687772397568 |
|---|---|
| author | McDiarmid, C Przykucki, M |
| author_facet | McDiarmid, C Przykucki, M |
| author_sort | McDiarmid, C |
| collection | OXFORD |
| description | Given a minor-closed class A of graphs, let βAdenote the supremum over all graphs in A of the ratio of edges to vertices. We investigate the set B of all such values βA, taking further the project begun by Eppstein. Amongst other results, we determine the small values in B (those up to 2); we show that B is ‘asymptotically dense’; and we answer some questions posed by Eppstein. |
| first_indexed | 2024-03-06T18:22:06Z |
| format | Journal article |
| id | oxford-uuid:06a7140a-ec24-4efb-bc75-d11a5a11d157 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:22:06Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:06a7140a-ec24-4efb-bc75-d11a5a11d1572022-03-26T09:03:39ZOn the critical densities of minor-closed classesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:06a7140a-ec24-4efb-bc75-d11a5a11d157Symplectic Elements at OxfordElsevier2018McDiarmid, CPrzykucki, MGiven a minor-closed class A of graphs, let βAdenote the supremum over all graphs in A of the ratio of edges to vertices. We investigate the set B of all such values βA, taking further the project begun by Eppstein. Amongst other results, we determine the small values in B (those up to 2); we show that B is ‘asymptotically dense’; and we answer some questions posed by Eppstein. |
| spellingShingle | McDiarmid, C Przykucki, M On the critical densities of minor-closed classes |
| title | On the critical densities of minor-closed classes |
| title_full | On the critical densities of minor-closed classes |
| title_fullStr | On the critical densities of minor-closed classes |
| title_full_unstemmed | On the critical densities of minor-closed classes |
| title_short | On the critical densities of minor-closed classes |
| title_sort | on the critical densities of minor closed classes |
| work_keys_str_mv | AT mcdiarmidc onthecriticaldensitiesofminorclosedclasses AT przykuckim onthecriticaldensitiesofminorclosedclasses |