Long cycles in random subgraphs of graphs with large minimum degree. Issue 4 (6th February 2015)

• Record Type: Journal Article
• Authors: Riordan, Oliver
• Is Part Of: Random structures & algorithms. Volume 45:Issue 4(2014)
• Page Start: 764
• Page End: 767
• Publication Date: 2015-02-06
• Subjects: random graphs -- long cycles; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20571
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: Let G be any graph of minimum degree at least k, and let G p be the random subgraph of G obtained by keeping each edge independently with probability p . Recently, Krivelevich, Lee and Sudakov showed that if pk → ∞ then with probability tending to 1 G p contains a cycle of length at least (1 – o (1)) k . We give a much shorter proof of this result, also based on depth‐first search. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 764–767, 2014