1,720,974 research outputs found
Ramsey multiplicity and the Tur\'an coloring
Get PDFExtending an earlier conjecture of Erd\H{o}s, Burr and Rosta conjectured that
among all two-colorings of the edges of a complete graph, the uniformly random
coloring asymptotically minimizes the number of monochromatic copies of any
fixed graph . This conjecture was disproved independently by Sidorenko and
Thomason. The first author later found quantitatively stronger counterexamples,
using the Tur\'an coloring, in which one of the two colors spans a balanced
complete multipartite graph.
We prove that the Tur\'an coloring is extremal for an infinite family of
graphs, and that it is the unique extremal coloring. This yields the first
determination of the Ramsey multiplicity constant of a graph for which the
Burr--Rosta conjecture fails.
We also prove an analogous three-color result. In this case, our result is
conditional on a certain natural conjecture on the behavior of two-color Ramsey
numbers.Comment: 39 pages, final version to appear in Advances in Combinatoric
Upper bounds on diagonal Ramsey numbers [after Campos, Griffiths, Morris, and Sahasrabudhe]
No full textRamsey\u27s theorem states that if is sufficiently large, then no matter how one colors the edges among vertices with two colors, there are always vertices spanning edges in only one color. Given this theorem, it is natural to ask ``how large is sufficiently large?\u27\u27 Ramsey\u27s original proof showed that is sufficient, and five years later Erdős and Szekeres improved this bound to . And then progress stalled for almost 90 years.
In this survey, I present the history of the problem and discuss some of the ideas used in the recent breakthrough of Campos--Griffiths--Morris--Sahasrabudhe, who proved that is sufficient. In addition, I discuss the subsequent work of Balister, Bollobás, Campos, Griffiths, Hurley, Morris, Sahasrabudhe, and Tiba, who gave an alternative, and more conceptual, proof.Expository paper accompanying a Bourbaki seminar talk (November 2024, exposé number 1230). 48 pages. Second version includes the follow-up of Balister et a
Ramsey numbers upon vertex deletion
Get PDFGiven a graph , its Ramsey number is the minimum so that every
two-coloring of contains a monochromatic copy of . It was
conjectured by Conlon, Fox, and Sudakov that if one deletes a single vertex
from , the Ramsey number can change by at most a constant factor. We
disprove this conjecture, exhibiting an infinite family of graphs such that
deleting a single vertex from each decreases the Ramsey number by a
super-constant factor.
One consequence of this result is the following. There exists a family of
graphs so that in any Ramsey coloring for (that is, a coloring
of a clique on vertices with no monochromatic copy of ), one of
the color classes has density .Comment: 11 page
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Ramsey numbers of books and quasirandomness
Get PDFThe book graph B^((k))_n consists of n copies of K_(k+1) joined along a common K_k. The Ramsey numbers of B^((k))_n are known to have strong connections to the classical Ramsey numbers of cliques. Recently, the first author determined the asymptotic order of these Ramsey numbers for fixed k, thus answering an old question of Erdős, Faudree, Rousseau, and Schelp. In this paper, we first provide a simpler proof of this theorem. Next, answering a question of the first author, we present a different proof that avoids the use of Szemerédi's regularity lemma, thus providing much tighter control on the error term. Finally, we prove a conjecture of Nikiforov, Rousseau, and Schelp by showing that all extremal colorings for this Ramsey problem are quasirandom
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
- …
