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The Triangle-Free Process and the Ramsey Number R(3,k)
The areas of Ramsey theory and random graphs have been closely linked ever since Erdős's famous proof in 1947 that the ""diagonal"" Ramsey numbers R(k) grow exponentially in k. In the early 1990s, the triangle-free process was introduced as a model which might potentially p...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
1920.
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| Colección: | Memoirs of the American Mathematical Society Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 001 | EBOOKCENTRAL_on1151199549 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
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| 008 | 200502s1920 riu o ||| 0 eng d | ||
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| 020 | |a 9781470456566 | ||
| 020 | |a 1470456567 | ||
| 029 | 1 | |a AU@ |b 000069467553 | |
| 035 | |a (OCoLC)1151199549 | ||
| 050 | 4 | |a QA164 |b .P668 2020 | |
| 082 | 0 | 4 | |a 511/.6 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Pontiveros, Gonzalo Fiz. | |
| 245 | 1 | 4 | |a The Triangle-Free Process and the Ramsey Number R(3,k) |h [electronic resource]. |
| 260 | |a Providence : |b American Mathematical Society, |c 1920. | ||
| 300 | |a 1 online resource (138 p.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society Ser. ; |v v.263 | |
| 500 | |a Description based upon print version of record. | ||
| 505 | 0 | |a Cover -- Title page -- Chapter 1. Introduction -- 1.1. Random graph processes -- 1.2. The triangle-free process -- Chapter 2. An overview of the proof -- Chapter 3. Martingale bounds: The line of peril and the line of death -- 3.1. The line of peril and the line of death -- 3.2. A general lemma -- 3.3. The events \X( ), \Y( ), \Z( ) and \Q( ) -- 3.4. Tracking ₑ -- Chapter 4. Tracking everything else -- 4.1. Building sequences -- 4.2. Self-correction -- 4.3. Creating and destroying copies of -- 4.4. Balanced non-tracking graph structures -- 4.5. Bounding the maximum change in *ᵩ( ) | |
| 505 | 8 | |a 4.6. The land before time = -- 4.7. Proof of Theorem 4.1 -- Chapter 5. Tracking ₑ, and mixing in the -graph -- 5.1. Mixing inside open neighbourhoods -- 5.2. Mixing in the whole -graph -- 5.3. Creating and destroying -walks -- 5.4. Self-correction -- 5.5. The Lines of Peril and Death -- Chapter 6. Whirlpools and Lyapunov functions -- 6.1. Whirlpools -- 6.2. Lyapunov functions -- 6.3. The proof of Theorems 2.1, 2.4, 2.5, 2.7 and 2.11 -- Chapter 7. Independent sets and maximum degrees in _{ ,\triangle} -- 7.1. A sketch of the proof -- 7.2. Partitioning the bad events | |
| 505 | 8 | |a 7.3. The events \A( , ) and \A'( , ) -- 7.4. The events \B( , )∩\D( , )^{ } and \B'( , )∩\D( , )^{ } -- 7.5. The events \C( , ) and \C'( , ) -- 7.6. The event \D( , ) -- 7.7. The proof of Propositions 7.1 and 7.2 -- Acknowledgements -- Bibliography -- Back Cover | |
| 520 | |a The areas of Ramsey theory and random graphs have been closely linked ever since Erdős's famous proof in 1947 that the ""diagonal"" Ramsey numbers R(k) grow exponentially in k. In the early 1990s, the triangle-free process was introduced as a model which might potentially provide good lower bounds for the ""off-diagonal"" Ramsey numbers R(3,k). In this model, edges of K_n are introduced one-by-one at random and added to the graph if they do not create a triangle; the resulting final (random) graph is denoted G_n,\triangle . In 2009, Bohman succeeded in following this process for a positive fra. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Ramsey theory. | |
| 650 | 0 | |a Combinatorial analysis. | |
| 650 | 6 | |a Théorie de Ramsey. | |
| 650 | 6 | |a Analyse combinatoire. | |
| 650 | 7 | |a Combinatorial analysis |2 fast | |
| 650 | 7 | |a Ramsey theory |2 fast | |
| 650 | 7 | |a Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX} -- Combinatorial probability -- Combinatorial probability. |2 msc | |
| 650 | 7 | |a Combinatorics {For finite fields, see 11Txx} -- Extremal combinatorics -- Ramsey theory [See also 05C55]. |2 msc | |
| 650 | 7 | |a Combinatorics {For finite fields, see 11Txx} -- Extremal combinatorics -- Probabilistic methods. |2 msc | |
| 700 | 1 | |a Griffiths, Simon. | |
| 700 | 1 | |a Morris, Robert. | |
| 758 | |i has work: |a The triangle-free process and the Ramsey number R(3, k) (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFrtcd8QD8Xq4FPxrt3TQC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Pontiveros, Gonzalo Fiz |t The Triangle-Free Process and the Ramsey Number R(3,k) |d Providence : American Mathematical Society,c1920 |z 9781470440718 |
| 830 | 0 | |a Memoirs of the American Mathematical Society Ser. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=6176737 |z Texto completo |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL6176737 | ||
| 994 | |a 92 |b IZTAP | ||