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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000428/type/journal_article |
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| Summary: | 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]). |
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| ISSN: | 2050-5094 |