Long cycles in random subgraphs of graphs with large minimum degree. Issue 4 (24th September 2014)

• Record Type: Journal Article
• Authors: Riordan, Oliver
• Is Part Of: Random structures & algorithms. Volume 45:Issue 4(2014)
• Page Start: 762
• Page End: 765
• Publication Date: 2014-09-24
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20571
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>Let <italic>G</italic> be any graph of minimum degree at least <italic>k</italic>, and let <italic>G</italic>_{<italic>p</italic>} be the random subgraph of <italic>G</italic> obtained by keeping each edge independently with probability <italic>p</italic>. Recently, Krivelevich, Lee and Sudakov showed that if <italic>pk</italic> → <italic>∞</italic> then with probability tending to 1 <italic>G</italic>_{<italic>p</italic>} contains a cycle of length at least (1 – <italic>o</italic>(1))<italic>k</italic>. We give a much shorter proof of this result, also based on depth‐first search. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 762–765, 2014</p> </abstract>