@inbook{fa92de54c95049a3960c2006790ae378,

title = "Cycle Saturation in Random Graphs",

abstract = "For a fixed graph F, the minimum number of edges in an edge-maximal F-free subgraph of G is called the F-saturation number. The asymptotics of the F-saturation number of the Erd{\"o}s–R{\'e}nyi random graph G(n, p) for constant p∈ (0, 1 ) was established for any complete graph and any star graph. We obtain the asymptotics of the Cm -saturation number of G(n, p) for m⩾ 5. Also we prove non-trivial linear (in n) lower bounds and upper bounds for the C4 -saturation number of G(n, p) for some fixed values of p.",

keywords = "Cycle, Extremal graph theory, Random graph, Saturation",

author = "Yury Demidovich and Maksim Zhukovskii",

note = "Funding Information: Acknowledgements. This work was carried out with the financial support of the Ministry of Education and Science of the Russian Federation, in the framework of Megagrant no. 075-15-2019-1926. The work of the first author was also supported by the Simons Foundation. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-83823-2_129",

language = "English (US)",

series = "Trends in Mathematics",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "811--816",

booktitle = "Trends in Mathematics",

address = "Germany",

}