FORCING QUASIRANDOMNESS WITH TRIANGLES
We study forcing pairs for quasirandom graphs. Chung, Graham, and Wilson initiated the study of families ${\mathcal{F}}$ of graphs with the property that if a large graph $G$ has approximately homomorphism density $p^{e(F)}$ for some fixed $p\in (0,1]$ for every $F\in {\mathcal{F}}$, then $G$ is qua...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2019-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509419000070/type/journal_article |
| _version_ | 1811156224972947456 |
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| author | CHRISTIAN REIHER MATHIAS SCHACHT |
| author_facet | CHRISTIAN REIHER MATHIAS SCHACHT |
| author_sort | CHRISTIAN REIHER |
| collection | DOAJ |
| description | We study forcing pairs for quasirandom graphs. Chung, Graham, and Wilson initiated the study of families ${\mathcal{F}}$ of graphs with the property that if a large graph $G$ has approximately homomorphism density $p^{e(F)}$ for some fixed $p\in (0,1]$ for every $F\in {\mathcal{F}}$, then $G$ is quasirandom with density $p$. Such families ${\mathcal{F}}$ are said to be forcing. Several forcing families were found over the last three decades and characterizing all bipartite graphs $F$ such that $(K_{2},F)$ is a forcing pair is a well-known open problem in the area of quasirandom graphs, which is closely related to Sidorenko’s conjecture. In fact, most of the known forcing families involve bipartite graphs only. |
| first_indexed | 2024-04-10T04:46:58Z |
| format | Article |
| id | doaj.art-342a2d126419451bbcfd1537968d7b9f |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:46:58Z |
| publishDate | 2019-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-342a2d126419451bbcfd1537968d7b9f2023-03-09T12:34:44ZengCambridge University PressForum of Mathematics, Sigma2050-50942019-01-01710.1017/fms.2019.7FORCING QUASIRANDOMNESS WITH TRIANGLESCHRISTIAN REIHER0MATHIAS SCHACHT1Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany; ,Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany; ,We study forcing pairs for quasirandom graphs. Chung, Graham, and Wilson initiated the study of families ${\mathcal{F}}$ of graphs with the property that if a large graph $G$ has approximately homomorphism density $p^{e(F)}$ for some fixed $p\in (0,1]$ for every $F\in {\mathcal{F}}$, then $G$ is quasirandom with density $p$. Such families ${\mathcal{F}}$ are said to be forcing. Several forcing families were found over the last three decades and characterizing all bipartite graphs $F$ such that $(K_{2},F)$ is a forcing pair is a well-known open problem in the area of quasirandom graphs, which is closely related to Sidorenko’s conjecture. In fact, most of the known forcing families involve bipartite graphs only.https://www.cambridge.org/core/product/identifier/S2050509419000070/type/journal_article05C80 |
| spellingShingle | CHRISTIAN REIHER MATHIAS SCHACHT FORCING QUASIRANDOMNESS WITH TRIANGLES Forum of Mathematics, Sigma 05C80 |
| title | FORCING QUASIRANDOMNESS WITH TRIANGLES |
| title_full | FORCING QUASIRANDOMNESS WITH TRIANGLES |
| title_fullStr | FORCING QUASIRANDOMNESS WITH TRIANGLES |
| title_full_unstemmed | FORCING QUASIRANDOMNESS WITH TRIANGLES |
| title_short | FORCING QUASIRANDOMNESS WITH TRIANGLES |
| title_sort | forcing quasirandomness with triangles |
| topic | 05C80 |
| url | https://www.cambridge.org/core/product/identifier/S2050509419000070/type/journal_article |
| work_keys_str_mv | AT christianreiher forcingquasirandomnesswithtriangles AT mathiasschacht forcingquasirandomnesswithtriangles |