WEAKLY SSATURATED SUBGRAPHS OF RANDOM GRAPHS
- Authors: Kalinichenko O.1, Tayfeh-Rezaie B.2, Zhukovskii M.1
- 
							Affiliations: 
							- Moscow Institute of Physics and Technology, Laboratory of Combinatorial and Geometric Structures
- School of Mathematics, Institute for Research in Fundamental Sciences (IPM)
 
- Issue: Vol 509 (2023)
- Pages: 46-49
- Section: MATHEMATICS
- URL: https://cardiosomatics.ru/2686-9543/article/view/647870
- DOI: https://doi.org/10.31857/S268695432370008X
- EDN: https://elibrary.ru/CTARUK
- ID: 647870
Cite item
Abstract
In this paper, we study weak saturation numbers of binomial random graphs. We proved stability of the weak saturation for several pattern graphs, and proved asymptotic stability for all pattern graphs.
Keywords
About the authors
O. Kalinichenko
Moscow Institute of Physics and Technology, Laboratory of Combinatorial and Geometric Structures
							Author for correspondence.
							Email: s15b1_kalinichenko@179.ru
				                					                																			                												                								Russia, Moscow						
B. Tayfeh-Rezaie
School of Mathematics, Institute for Research in Fundamental Sciences (IPM)
							Author for correspondence.
							Email: tayfeh-r@ipm.ir
				                					                																			                												                								Iran, Tehran						
M. Zhukovskii
Moscow Institute of Physics and Technology, Laboratory of Combinatorial and Geometric Structures
							Author for correspondence.
							Email: zhukmax@gmail.com
				                					                																			                												                								Russia, Moscow						
References
- Alon N. An extremal problem for sets with applications to graph theory // J. Combin. Theory Ser. A. 1985. V. 40. № 1. P. 82–89.
- Bidgoli M.R., Mohammadian A., Tayfeh-Rezaie B., Zhukovskii M. Threshold for weak saturation stability // arXiv:2006.06855. 2020.
- Bollobás B. Weakly k-saturated graphs // Beiträge zur Graphen–theorie. 1968. P. 25–31.
- Kalai G. Hyperconnectivity of graphs // Graphs Combin. 1985 V. 1. P. 65–79.
- Kalinichenko O., Zhukovskii M. Weak saturation stability // arXiv:2107.11138. 2022.
- Korándi D., Sudakov B. Saturation in random graphs // Random Structures Algorithms. 2017. V. 51. № 1. P. 169–181.
- Krivelevich M., Patkós B. Equitable coloring of random graphs // Random Structures Algorithms. 2009. V. 35. № 1. P. 83–99.
- Kronenberg, G., Martins T., Morrison N. Weak saturation numbers of complete bipartite graphs in the clique // J. Combin. Theory Ser. A. 2021. V. 178. 105357.
- Lovász, L. Flats in matroids and geometric graphs // Combinatorial Surveys. 1977. P. 45–86.
- Spencer J. Threshold Functions for Extension Statements // J. Combin. Theory Ser. A. 1990. V. 53. P. 286–305.
Supplementary files
 
				
			 
					 
						 
						 
						 
						 
									

 
  
  
  Email this article
			Email this article 

 Open Access
		                                Open Access Access granted
						Access granted Subscription or Fee Access
		                                							Subscription or Fee Access
		                                					