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@article{2392301, author = {Balogh, Jozsef and Lamaison Vidarte, Ander}, article_location = {DURHAM}, article_number = {1}, doi = {http://dx.doi.org/10.1215/00192082-10450499}, keywords = {Ramsey theory; Ramsey upper density}, language = {eng}, issn = {0019-2082}, journal = {Illinois Journal of Mathematics}, title = {Ramsey upper density of infinite graph factors}, url = {http://dx.doi.org/10.1215/00192082-10450499}, volume = {67}, year = {2023} }
TY - JOUR ID - 2392301 AU - Balogh, Jozsef - Lamaison Vidarte, Ander PY - 2023 TI - Ramsey upper density of infinite graph factors JF - Illinois Journal of Mathematics VL - 67 IS - 1 SP - 171-184 EP - 171-184 PB - Duke University Press SN - 00192082 KW - Ramsey theory KW - Ramsey upper density UR - http://dx.doi.org/10.1215/00192082-10450499 N2 - 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. ER -
BALOGH, Jozsef and Ander LAMAISON VIDARTE. Ramsey upper density of infinite graph factors. \textit{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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