Density of monochromatic infinite subgraphs II
In 1967, Gerencsér and Gyárfás [16] proved a result which is considered the starting point of graph-Ramsey theory: In every 2-coloring of $K_n$ , there is a monochromatic path on $\lceil (2n+1)/3\rceil $ vertices, and this is best possible. There have since been hundreds of papers on gr...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000428/type/journal_article |
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| author | Jan Corsten Louis DeBiasio Paul McKenney |
| author_facet | Jan Corsten Louis DeBiasio Paul McKenney |
| author_sort | Jan Corsten |
| collection | DOAJ |
| description | In 1967, Gerencsér and Gyárfás [16] proved a result which is considered the starting point of graph-Ramsey theory: In every 2-coloring of
$K_n$
, there is a monochromatic path on
$\lceil (2n+1)/3\rceil $
vertices, and this is best possible. There have since been hundreds of papers on graph-Ramsey theory with some of the most important results being motivated by a series of conjectures of Burr and Erdős [2, 3] regarding the Ramsey numbers of trees (settled in [31]), graphs with bounded maximum degree (settled in [5]), and graphs with bounded degeneracy (settled in [23]). |
| format | Article |
| id | doaj-art-e9b6956262dc459f8ba30b466a2db607 |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-e9b6956262dc459f8ba30b466a2db6072025-08-20T03:47:33ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.42Density of monochromatic infinite subgraphs IIJan Corsten0https://orcid.org/0000-0002-1114-5657Louis DeBiasio1https://orcid.org/0000-0002-7569-7952Paul McKenney2Department of Mathematics, London School of Economics and Political Science (LSE), London, United Kingdom; E-mail:Department of Mathematics, Miami University, Oxford, OH, United StatesDepartment of Mathematics, Miami University, Oxford, OH, United States; E-mail:In 1967, Gerencsér and Gyárfás [16] proved a result which is considered the starting point of graph-Ramsey theory: In every 2-coloring of $K_n$ , there is a monochromatic path on $\lceil (2n+1)/3\rceil $ vertices, and this is best possible. There have since been hundreds of papers on graph-Ramsey theory with some of the most important results being motivated by a series of conjectures of Burr and Erdős [2, 3] regarding the Ramsey numbers of trees (settled in [31]), graphs with bounded maximum degree (settled in [5]), and graphs with bounded degeneracy (settled in [23]).https://www.cambridge.org/core/product/identifier/S2050509425000428/type/journal_article05C5503E05 |
| spellingShingle | Jan Corsten Louis DeBiasio Paul McKenney Density of monochromatic infinite subgraphs II Forum of Mathematics, Sigma 05C55 03E05 |
| title | Density of monochromatic infinite subgraphs II |
| title_full | Density of monochromatic infinite subgraphs II |
| title_fullStr | Density of monochromatic infinite subgraphs II |
| title_full_unstemmed | Density of monochromatic infinite subgraphs II |
| title_short | Density of monochromatic infinite subgraphs II |
| title_sort | density of monochromatic infinite subgraphs ii |
| topic | 05C55 03E05 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425000428/type/journal_article |
| work_keys_str_mv | AT jancorsten densityofmonochromaticinfinitesubgraphsii AT louisdebiasio densityofmonochromaticinfinitesubgraphsii AT paulmckenney densityofmonochromaticinfinitesubgraphsii |