Distribution of the number of spanning regular subgraphs in random graphs1. Issue 3 (4th April 2012)

• Record Type: Journal Article
• Authors: Gao, Pu
• Is Part Of: Random structures & algorithms. Volume 43:Issue 3(2013)
• Page Start: 338
• Page End: 353
• Publication Date: 2012-04-04
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20418
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>In this paper, we examine the moments of the number of <italic>d</italic> ‐factors in <tex-math notation="LaTeX"><![CDATA[\documentclass{article}\usepackage{mathrsfs, amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}\mathcal{ G}(n, p)\end{align*} \end{document}]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg2pr8ckgs" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> for all <italic>p</italic> and <italic>d</italic> satisfying <italic>d</italic>³ = <italic>o</italic>(<italic>p</italic>²<italic>n</italic>). We also determine the limiting distribution of the number of <italic>d</italic> ‐factors inside this range with further restriction that <tex-math notation="LaTeX"><![CDATA[\documentclass{article}\usepackage{mathrsfs, amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}(1-p)\sqrt{dn}\to\infty\end{align*} \end{document}]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg2pr8ckhb" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> as <italic>n</italic> →<italic>∞</italic>.© 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013</p> </abstract>