BALOGH, Jozsef and Ander LAMAISON VIDARTE. Ramsey upper density of infinite graph factors. Illinois Journal of Mathematics. DURHAM: Duke University Press, 2023, vol. 67, No 1, p. 171-184. ISSN 0019-2082. Available from: https://dx.doi.org/10.1215/00192082-10450499.
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Basic information
Original name Ramsey upper density of infinite graph factors
Authors BALOGH, Jozsef and Ander LAMAISON VIDARTE (724 Spain, belonging to the institution).
Edition Illinois Journal of Mathematics, DURHAM, Duke University Press, 2023, 0019-2082.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10201 Computer sciences, information science, bioinformatics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW URL
Impact factor Impact factor: 0.600 in 2022
RIV identification code RIV/00216224:14330/23:00133945
Organization unit Faculty of Informatics
Doi http://dx.doi.org/10.1215/00192082-10450499
UT WoS 000975697100008
Keywords in English Ramsey theory; Ramsey upper density
Tags International impact, Reviewed
Changed by Changed by: RNDr. Pavel Šmerk, Ph.D., učo 3880. Changed: 8/4/2024 11:48.
Abstract
The study of upper density problems on Ramsey theory was initiated by Erdos and Galvin in 1993 in the particular case of the infinite path, and by DeBiasio and McKenney in general. In this paper, we are concerned with the following problem: given a fixed finite graph F, what is the largest value of n, such that every 2-edge-coloring of the complete graph on N contains a monochromatic infinite F-factor whose vertex set has upper density at least A? Here we prove a new lower bound for this problem. For some choices of F, including cliques and odd cycles, this new bound is sharp because it matches an older upper bound. For the particular case where F is a triangle, we also give an explicit lower bound of 1- p 1 7 = 0.62203 ... , improving the previous best bound of 3/5.
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