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Saturation problems in the Ramsey theory of graphs, posets and point sets

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Title
Saturation problems in the Ramsey theory of graphs, posets and point sets
Author(s)
Damásdi, Gábor; Keszegh, Balázs; Malec, David; Casey Tompkins; Wang, Zhiyu; Zamora, Oscar
Publication Date
2021-06
Journal
EUROPEAN JOURNAL OF COMBINATORICS, v.95
Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Abstract
© 2021 Elsevier Ltd. All rights reserved. In 1964, Erdos, Hajnal and Moon introduced a saturation version of Tur & aacute;n's classical theorem in extremal graph theory. In particular, they determined the minimum number of edges in a Kr-free, n-vertex graph with the property that the addition of any further edge yields a copy of Kr. We consider analogues of this problem in other settings. We prove a saturation version of the Erdos-Szekeres theorem about monotone subsequences and saturation versions of some Ramsey-type theorems on graphs and Dilworth-type theorems on posets. We also consider semisaturation problems, wherein we allow the family to have the forbidden configuration, but insist that any addition to the family yields a new copy of the forbidden configuration. In this setting, we prove a semisaturation version of the Erdos-Szekeres theorem on convex k-gons, as well as multiple semisaturation theorems for sequences and posets. (c) 2021 Elsevier Ltd. All rights reserved.
URI
https://pr.ibs.re.kr/handle/8788114/10033
DOI
10.1016/j.ejc.2021.103321
ISSN
0195-6698
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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