Matches in SemOpenAlex for { <https://semopenalex.org/work/W2507398958> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W2507398958 abstract "It is known that every graph of sufficiently large chromatic number and bounded clique number contains, as an induced subgraph, a subdivision of any fixed forest, and a subdivision of any fixed cycle. Equivalently, forests and triangles are pervasive, where H is pervasive (in some class of graphs) if for all s>0, every graph in the class with bounded clique number and sufficiently large chromatic number contains an induced subdivision of H, with every edge subdivided at least s times. Which other graphs are pervasive? Chalopin, Esperet, Li and Ossona de Mendez proved that every such graph is a forest of lanterns: roughly, the blocks are lanterns (graphs obtained from a tree by adding one extra vertex), and there are rules about how blocks fit together. It is not known whether every forest of lanterns is pervasive; but in another paper two of us prove that banana trees (multigraphs obtained from a forest by adding parallel edges) are pervasive, thus generalizing the two results above. This paper contains the first half of the proof, which works for any forest of lanterns, not just for banana trees. A class of graphs is r-controlled if for every graph in the class, its chromatic number is at most some function (determined by the class) of the largest chromatic number of an r-ball in the graph. In this paper we prove that for all r>1, every forest of lanterns is pervasive in every r-controlled class These results turn out particularly nicely when applied to string graphs (intersection graphs of sets of curves in the plane). A chandelier is a graph obtained from a tree by adding a vertex adjacent to its leaves. We prove that the class of string graphs is 2-controlled, and thus forests of lanterns are pervasive in this class. Furthermore, string graphs of sufficiently large chromatic number and bounded clique number contain any fixed chandelier as an induced subgraph." @default.
- W2507398958 created "2016-09-16" @default.
- W2507398958 creator A5028345325 @default.
- W2507398958 creator A5031948088 @default.
- W2507398958 creator A5045091550 @default.
- W2507398958 date "2016-09-01" @default.
- W2507398958 modified "2023-10-03" @default.
- W2507398958 title "Induced subgraphs of graphs with large chromatic number. V. Chandeliers and strings" @default.
- W2507398958 cites W1852112098 @default.
- W2507398958 cites W1910630822 @default.
- W2507398958 cites W1975403516 @default.
- W2507398958 cites W2004008828 @default.
- W2507398958 cites W2022000813 @default.
- W2507398958 cites W2104090107 @default.
- W2507398958 cites W2144710149 @default.
- W2507398958 cites W2582848504 @default.
- W2507398958 cites W2612220480 @default.
- W2507398958 cites W2768160776 @default.
- W2507398958 cites W2768885882 @default.
- W2507398958 cites W3101282841 @default.
- W2507398958 cites W968859509 @default.
- W2507398958 hasPublicationYear "2016" @default.
- W2507398958 type Work @default.
- W2507398958 sameAs 2507398958 @default.
- W2507398958 citedByCount "7" @default.
- W2507398958 countsByYear W25073989582015 @default.
- W2507398958 countsByYear W25073989582017 @default.
- W2507398958 countsByYear W25073989582018 @default.
- W2507398958 countsByYear W25073989582020 @default.
- W2507398958 countsByYear W25073989582021 @default.
- W2507398958 crossrefType "posted-content" @default.
- W2507398958 hasAuthorship W2507398958A5028345325 @default.
- W2507398958 hasAuthorship W2507398958A5031948088 @default.
- W2507398958 hasAuthorship W2507398958A5045091550 @default.
- W2507398958 hasConcept C114614502 @default.
- W2507398958 hasConcept C118615104 @default.
- W2507398958 hasConcept C132525143 @default.
- W2507398958 hasConcept C134306372 @default.
- W2507398958 hasConcept C143392562 @default.
- W2507398958 hasConcept C166957645 @default.
- W2507398958 hasConcept C196956537 @default.
- W2507398958 hasConcept C205649164 @default.
- W2507398958 hasConcept C33923547 @default.
- W2507398958 hasConcept C34388435 @default.
- W2507398958 hasConcept C80899671 @default.
- W2507398958 hasConceptScore W2507398958C114614502 @default.
- W2507398958 hasConceptScore W2507398958C118615104 @default.
- W2507398958 hasConceptScore W2507398958C132525143 @default.
- W2507398958 hasConceptScore W2507398958C134306372 @default.
- W2507398958 hasConceptScore W2507398958C143392562 @default.
- W2507398958 hasConceptScore W2507398958C166957645 @default.
- W2507398958 hasConceptScore W2507398958C196956537 @default.
- W2507398958 hasConceptScore W2507398958C205649164 @default.
- W2507398958 hasConceptScore W2507398958C33923547 @default.
- W2507398958 hasConceptScore W2507398958C34388435 @default.
- W2507398958 hasConceptScore W2507398958C80899671 @default.
- W2507398958 hasOpenAccess W2507398958 @default.
- W2507398958 hasRelatedWork W1964982423 @default.
- W2507398958 hasRelatedWork W2012767915 @default.
- W2507398958 hasRelatedWork W2022000813 @default.
- W2507398958 hasRelatedWork W2066125721 @default.
- W2507398958 hasRelatedWork W2072964213 @default.
- W2507398958 hasRelatedWork W2082797962 @default.
- W2507398958 hasRelatedWork W2104090107 @default.
- W2507398958 hasRelatedWork W2129193084 @default.
- W2507398958 hasRelatedWork W281717368 @default.
- W2507398958 hasRelatedWork W2911678318 @default.
- W2507398958 hasRelatedWork W2951507227 @default.
- W2507398958 hasRelatedWork W2962706559 @default.
- W2507398958 hasRelatedWork W3003350215 @default.
- W2507398958 hasRelatedWork W3029731269 @default.
- W2507398958 hasRelatedWork W3093461576 @default.
- W2507398958 hasRelatedWork W3099405462 @default.
- W2507398958 hasRelatedWork W3101282841 @default.
- W2507398958 hasRelatedWork W968859509 @default.
- W2507398958 hasRelatedWork W2183572846 @default.
- W2507398958 hasRelatedWork W2413066628 @default.
- W2507398958 isParatext "false" @default.
- W2507398958 isRetracted "false" @default.
- W2507398958 magId "2507398958" @default.
- W2507398958 workType "article" @default.